# How Well Do You Know Short Cuts To Finding Squares

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Finding squares is most people's nightmare judging by the fact that not everyone is meant to be a math guru. Fortunately there are ways to find squares without the help of a calculator. This means that you will not have to memorize the "magic" keys on your calculator but namely know a trick or two that will stick to your head forever. Take our quiz and see if you can figure those tricks out.

• 1.

### What are most shortcuts into finding a square based off?

• A.

(a+b) = a^2 + b^2 + 2*a*b

• B.

A^2 + b^2 + 2*a*b

• C.

(a+b)^2= a^2 + b^2 + 2*a*b

• D.

B^2= a^2 + b^2 + 2*a*b

C. (a+b)^2= a^2 + b^2 + 2*a*b
Explanation
The correct answer is (a+b)^2= a^2 + b^2 + 2*a*b. This is the formula for squaring a binomial, where (a+b)^2 is equal to a^2 + b^2 + 2*a*b. This can be derived using the distributive property and multiplying each term in the binomial by itself.

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• 2.

### What's the first step into finding the square of 2 digit number which ends in 5?

• A.

Multiply the first digit of the number with the next to its number.

• B.

Multiply the last digit of the number with the next to its number.

• C.

Divide the first digit of the number with the next to its number.

• D.

Substract the first digit of the number with the next to its number.

A. Multiply the first digit of the number with the next to its number.
Explanation
To find the square of a two-digit number that ends in 5, the first step is to multiply the first digit of the number with the next digit. For example, if the number is 25, the first digit is 2 and the next digit is 5, so multiplying them gives 2*5=10. This step is necessary because when a number ends in 5, its square always ends in 25.

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• 3.

### What's the second step into squaring any 2 digit number?

• A.

To go down 5 from the answer found on step 1.

• B.

To go up 3 from the answer found on step 1.

• C.

To go down 3 from the answer found on step 1.

• D.

To go down 2 from the answer found on step 1.

C. To go down 3 from the answer found on step 1.
Explanation
The second step in squaring any 2-digit number is to go down 3 from the answer found in step 1.

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• 4.

### What is the first step into finding the square of a number between 30 to 79?

• A.

Find how many more or less the given number is from 30.

• B.

Find how many more or less the given number is from 50.

• C.

Find how many more or less the given number is from 70.

• D.

Find how many more or less the given number is from 100.

B. Find how many more or less the given number is from 50.
Explanation
To find the square of a number between 30 to 79, the first step is to find how many more or less the given number is from 50. This step is important because it helps us determine the difference between the given number and the midpoint (50) of the range. By finding this difference, we can then proceed to calculate the square of the number using the appropriate formula or method.

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• 5.

### What is the second step into finding the square of a number between 30 to 79?

• A.

Add the number 25 if more than 50 or subtract the number from 25 if less than 50.

• B.

Subtract the number 25 if more than 50 or add the number from 25 if less than 50.

• C.

Multiply the number 25 if more than 50 or subtract the number from 25 if less than 50.

• D.

Add the number 25 if more than 50 or multiply the number from 25 if less than 50.

A. Add the number 25 if more than 50 or subtract the number from 25 if less than 50.
Explanation
To find the square of a number between 30 to 79, the second step is to add the number 25 if the number is more than 50 or subtract the number from 25 if the number is less than 50. This step is necessary to adjust the value of the number before squaring it.

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• 6.

### What's the last step into finding the square of a number between 30 to 79?

• A.

Find the square of the number added or subtracted and put next to the result arrived at in step 2.

• B.

Find the square of the number added or subtracted and put next to the result arrived at in step 1.

• C.

Find the square of the number added and put next to the result arrived at in step 2.

• D.

Find the square of the number subtracted and put next to the result arrived at in step 1.

A. Find the square of the number added or subtracted and put next to the result arrived at in step 2.
Explanation
To find the square of a number between 30 to 79, we need to follow the steps mentioned in the answer. First, we find the square of the number added or subtracted, and then we put it next to the result arrived at in step 2. This implies that we perform some operation on the number, either addition or subtraction, and then find its square. Finally, we place this squared value next to the result obtained in step 2.

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• 7.

### What's the first step into mentally square any number from 20 to 29?

• A.

Add given number and the unit's digit.

• B.

Add 20 to the given number and the unit's digit.

• C.

Add 25 to the given number and the unit's digit.

• D.

Substract given number and the unit's digit.

A. Add given number and the unit's digit.
Explanation
To mentally square any number from 20 to 29, the first step is to add the given number and the unit's digit. This is because when you square a number, you are multiplying it by itself. Adding the given number and the unit's digit helps to simplify the calculation and make it easier to mentally square the number.

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• 8.

### What's the second step into mentally square any number from 20 to 29?

• A.

Tripple the result obtained in step 1

• B.

Double the result obtained in step 1

• C.

Divide the result obtained in step 1 by 10.

• D.

Divide the result obtained in step 1 by 2.

B. Double the result obtained in step 1
Explanation
The second step into mentally square any number from 20 to 29 is to double the result obtained in step 1.

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• 9.

### What's the third step into mentally square any number from 20 to 29?

• A.

Square the unit's digit of the number given and place it next to the result obtained in step 1.

• B.

Divide the result obtained in step 1 by 10.

• C.

Square the unit's digit of the number given and place it next to the result obtained in step 2.

• D.

Square the unit's digit of the number given and place it next to the result obtained in step 3.

C. Square the unit's digit of the number given and place it next to the result obtained in step 2.
Explanation
The third step into mentally squaring any number from 20 to 29 is to square the unit's digit of the number given and place it next to the result obtained in step 2.

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• 10.

### What's the second step into finding the square of any number between 10 and 19?

• A.

Square the unit's digit and put the number next to the result obtained in step 1.

• B.

Square the unit's digit and put the number next to the result obtained in step 2.

• C.

Square the unit's digit and put the number next to the result obtained in step 3.

• D.

Double the unit's digit and put the number next to the result obtained in step 1.

A. Square the unit's digit and put the number next to the result obtained in step 1.
Explanation
The second step in finding the square of any number between 10 and 19 is to square the unit's digit and put the number next to the result obtained in step 1.

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• Current Version
• Mar 19, 2023
Quiz Edited by
ProProfs Editorial Team
• Jun 06, 2018
Quiz Created by
Anouchka

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