Question

How do you simplify $\sqrt{0.36}$?

Answer 1

We try to form the indices formula for the value 2. This is a square root of $0.36$. We convert the decimal to fractions. The root of the whole fraction happens by finding the root of the denominator and numerator separately as $\sqrt{\dfrac{p}{q}}=\dfrac{\sqrt{p}}{\sqrt{q}}$.
We find the root values and place to find the solution. We find the prime factorisation of 36 and 100.

Complete step by step solution:
We need to find the value of the algebraic form of $\sqrt{0.36}$. This is a square root form.
The given value is the form of indices. We are trying to find the root value of $0.36$.
We know the theorem of indices ${{a}^{\dfrac{1}{n}}}=\sqrt[n]{a}$. Putting value 2 we get
${{a}^{\dfrac{1}{2}}}=\sqrt{a}$.
Converting decimal to fraction we get $0.36=\dfrac{36}{100}$.
We have to solve the answer of $\sqrt{\dfrac{36}{100}}$. We know
$\sqrt{\dfrac{p}{q}}=\dfrac{\sqrt{p}}{\sqrt{q}}$.
This means to find the answer of $\sqrt{\dfrac{36}{100}}$, we need to find $\sqrt{36}$ and
$\sqrt{100}$.
For $\sqrt{36}=\sqrt{{{\left( 6 \right)}^{2}}}=6$ and for $\sqrt{100}=\sqrt{{{\left( 10 \right)}^{2}}}=10$
We now place the values and get
$\sqrt{\dfrac{36}{100}}=\dfrac{\sqrt{36}}{\sqrt{100}}=\dfrac{6}{10}=\dfrac{3}{5}$.
Now we convert the fraction into fraction and get $\dfrac{3}{5}=0.6$
The simplified value of the square root $\sqrt{0.36}$ is $0.6$.

Note: We can also use the variable from where we can take $x={{\left( 0.36 \right)}^{\dfrac{1}{2}}}$. But we need to remember that we can’t use the square on both sides of the equation $x={{\left( 0.36 \right)}^{\dfrac{1}{2}}}$ as in that case we are taking an extra value of negative as in $0.36$ as a root value. Then this linear equation becomes a quadratic equation.