Question

How do you simplify $\sqrt{\dfrac{24}{25}}$ ?

Answer 1

Hint: Now we are given with an expression containing root. First we will factorize the numerator and denominator into prime factors and then we will take out the squares from the root. Hence we will get the simplified expression.

Complete step by step answer:
Let us first understand the concept of square and square root. Now square of a number means the number multiplied by itself. Hence square of 2 will be $2\times 2=4$ . Square of a number x is denoted by ${{x}^{2}}$ .
Now similarly square root is the inverse function of square. Hence the square root of 64 is 8 as $8\times 8=64$ . Square root of 64 can be denoted by $\sqrt{64}$ .
Now consider the given expression $\sqrt{\dfrac{24}{25}}$
Now the given expression has a fraction inside a root.
We want to simplify the given expression.
First we will factorize the numerator and denominator of the fraction.
We know that $24=2\times 2\times 2\times 3$ and $25=5\times 5$
Now since we want to remove terms from square root we will try to write the numbers in squares.
Hence we can say that $24={{2}^{2}}\times 6$ and $25={{5}^{2}}$
Now substituting this in the given expression we get,
$\Rightarrow \sqrt{\dfrac{{{2}^{2}}\times 6}{{{5}^{2}}}}$
Now we know that $\sqrt{{{x}^{2}}}=x$ Hence we can take out 2 and 5 from the root.
Hence we get the given expression as $\dfrac{2}{5}\sqrt{6}$

Hence the given expression can be written as $\dfrac{2\sqrt{6}}{5}$.

Note: Now note that when 2 is in power we call it square. Similarly if we have 3 in power then we call it a cube. Now we can denote cube root of a number x by $\sqrt[3]{x}$ . Similarly we can denote ${{n}^{th}}$ root of any number.