Question

How do you simplify the square root of 21 times the square root of 24?

Answer 1

Hint: The problem is based on the square root of the integers.
By square root we mean that the number or variable is raised to power 1/2.
We will discuss square roots in more detail to solve the given problem.

Complete step-by-step solution:
Square root means the variable or number is raised to power 1/2.
Let’s understand square root in more detail;
$ \Rightarrow \sqrt {x.x} $ (x and x is multiplied twice under the square root)
$ \Rightarrow {({x^2})^{\dfrac{1}{2}}}$ (The above value can be written like this)
$ \Rightarrow x$
This is how square root is calculated when a number or variable is given.
We are given in question;
$ \Rightarrow \sqrt {21} .\sqrt {24} $
In order to calculate the given problem we will expand the numbers written in square root.
$ \Rightarrow \sqrt {3 \times 7} .\sqrt {2 \times 2 \times 2 \times 3} $ (Both the terms are written in square root, so we have multiplied the two)
$ \Rightarrow \sqrt {3 \times 7 \times 2 \times 2 \times 2 \times 3} $ (The numbers which are repeated twice will have power 1)
$ \Rightarrow 6\sqrt {14} $ (2 and 3 are repeated and the rest will remain inside the square root)

$6\sqrt {14} $ is a simplified answer of the given expression.

Note: In order to solve such problems we must remember a few square roots which are common to use and make our calculations fast, as of 121, 169, 196 , 225 , 256 , 289 (11, 13 , 14, 15, 16, 17 are their square roots). Like the square root means power half in the similar manner cube root means power 1/3.In the similar way few cube roots which we must remember are 8, 27 , 125, 64, 216, 343, 512 (2, 3, 5, 4, 6,7. 8 are required cube roots )