Square root of 117

The approximate value of √117 is 10.816653. In its exponential form, we write it as → (117)½. 
Let’s now learn more about the square root of 117. 
 

Children learn different methods to solve square roots. Few methods are well-used and approved. These methods are explained below. 
 

Here, we break the numbers into their prime factors.

Prime factorization of 117; 

117= 3×3×13 

All prime factors cannot be paired and 117 cannot be simplified to a perfect square. Hence, the square root of 117 cannot be expressed in simple radical form. 

√117= ∛13
 

For non-perfect squares, we often use the nearest perfect square value to find the value of a square root. Follow the below steps; 

Step 1: Write the number 117 to perform a long division.

Step 2: Find a perfect square number that is less than or equal to 117. For 117, the number is 100 (10²). 

Step 3: Divide 117 by 10. The remainder will be 17 and quotient will be 10.

Step 4: Bring down the remainder (17) and add two zeros. Add a decimal point to the quotient, it becomes 10.0.
Step 5: Double the quotient and use it as the new divisor. 

Step 6: Pick a number that will complete the divisor so that when it is multiplied by. The product will be less than or equal to 1700. 

Step 7: Continue to the division to find the √117 to as many decimal places as necessary. 
→ √117 = 10.816653
 

In the approximation method, we estimate the square root by considering the closest perfect square to 117. 
Follow the below steps; 

Step 1: Nearest perfect square to 117 → √100=10 and √121=11

Step 2: 117 falls between 100 and 121 therefore the square root falls between 10 and 11

Step 3: We try to test numbers like 10.5,10.6 and further. We find that √117 = 10.816. 
 

• Prime numbers — Any number that has only two factors, 1 and the number itself, is called a prime number. Prime numbers up to 10 are — 2,3,5,7.

• Integer — A number between zero and infinite, that can be positive or negative, fraction or decimal. 

• Rational numbers — A number that can be expressed in p/q form and where both p and q are integers and q (the denominator) is not equal to 0. 

• Irrational numbers — A number that cannot be expressed in the p/q form where q is equal to 0 is called an irrational number. 

• Perfect square number — a number whose square root has no decimal places in them. 

• Non-perfect square numbers — A number whose square has a fraction or decimal in its result.