Question

How do you simplify the square root of the number 750?

Answer 1

Hint: We start solving the problem by writing the square root of 750 as a variable. We then write 750 as the multiplication of two numbers. We then make use of the fact that \[\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\] to proceed through the problem. We then write the number in the square root of the obtained result as a multiplication of two numbers and then make use of the fact that \[\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\] to get the simplified form.

Complete step-by-step solution:
According to the problem, we are asked to find the square root of the number 750.
Let us assume $s=\sqrt{750}$.
$\Rightarrow s=\sqrt{25\times 30}$ ---(1).
We can see that the equation (1) resembles the form $\sqrt{a\times b}$. We know that \[\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\]. Let us use this result in equation (1).
$\Rightarrow s=\sqrt{25}\times \sqrt{30}$ ---(2).
We know that $\sqrt{25}=5$. Let us use this result in equation (2).
$\Rightarrow s=5\times \sqrt{30}$.
\[\Rightarrow s=5\times \sqrt{100\times 0.3}\] ---(3).
We can see that $\sqrt{100\times 0.3}$ in equation (3) resembles the form $\sqrt{a\times b}$. We know that \[\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\]. Let us use this result in equation (3).
$\Rightarrow s=5\times \sqrt{100}\times \sqrt{0.3}$ ---(4).
We know that $\sqrt{100}=10$. Let us use this result in equation (4).
$\Rightarrow s=5\times 10\times \sqrt{0.3}$.
$\Rightarrow s=50\sqrt{0.3}$.
$\therefore $ We have found the simplified form of the square root of the value of 750 as $50\sqrt{0.3}$.

Note: Whenever we get this type of problems, we try to make use of the fact \[\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\] to make the process simpler. We can also simplify the answer further but we cannot get the exact answer for the square root. We can also find an estimate of the square root by making use of the long division method. Similarly, we can expect problems to find the square root of the number 1000 using a long division method up to 3 decimals.