The square root of 117 in simplified radical form is 3√13. Mathematically, the square root of 117 can be expressed as √117. In this post, we will learn how to find the square root of 117 in its simplest form.

The formula of root 117 simplified is given below:

√117 = 3√13.

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**Square root of 117 in Simplest Radical Form**

**Answer:** 3√13 is the simplest radical form of square root 117.

**Solution:**

To find the square root of 117 in its simplest radical form, we will write 117 as a product of two numbers; at least one of them will be a perfect square.

A few perfect squares are 1, 4, 9, 16, 25, etc. Note that 9 divides 117, and we write 117 as

117 = 9 × 13.

Taking square root on both sides, we get that

$\sqrt{117}=\sqrt{9 \times 13}$

⇒ $\sqrt{117}$ $=\sqrt{9} \times \sqrt{13}$ using the formula √(a×b) = √a × √b.

= 3 × √13 as we know that the square root of 9 is 3.

= 3√13

Therefore, the square root of 117 in simplified radical form is equal to 3√13.

**Have You Read These Simplified Square Roots?**

## FAQs on Square Root of 117

**Q1: What is the square root of 117 in simplified radical form?**

**Answer**: Note that 117 can be factored as 117 = 3 × 3 × 13. Thus, the square root of 117 is equal to √(3 × 3 × 13) = 3√13. So 3√13 is the simplified radical form of square root of 117.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.