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If the index of a positive number x is half √x then it is known as **square root **of x.

How to solve square roots: -

**Question 1**: - Find the square root of 384 (or √384)

How to solve square roots: -

Steps | Solution |

Step 1: - Try to factorize a 384 to their possible smallest value. |
384 can be written as 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 |

Step 2: - Choose the pair of numbers. |
There are three pairs of 2 and the remaining 2 unpaired numbers are 2 and 3 like, (2 x 2) x (2 x 2) x (2 x 2) x (2 x 3) |

Step 3: - Take out the pair of a number as a single number. |
3 pair of 2 will come outside the square root and will be written as a single number. 2 x 2 x 2 x √ ( 2 x 3) |

Step4: - Multiply the numbers which is outside and inside the square root separately. | √384 = 8 √6 (since 2x2x2 =8 and 2 x 3 = 6) |

Therefore √384 = 8 √6

√ 27 = √ (3 x 3 x 3) = 3 √3

Therefore, 27 = 3 √3.

√64 = √ (2 x 2 x 2 x 2 x 2 x 2) = 2 x 2 x 2 = 8

Therefore √ 64 = 8