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

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

⇒ $\sqrt{117}$ $=\sqrt{9} \times \sqrt{117}$ 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.

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## 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.