simplify $\sqrt{90\}$
You asked:
Simplify the expression: \(\sqrt{90}\)
MathBot Answer:
\[\sqrt{90} = 3 \sqrt{10}\]
Given a positive integer \(n\), \(\sqrt{n}\) simplifies to \(\sqrt{n} = p \sqrt{q}\) if \(n\) can be written as the product \(n = p^2 q\), where \(p\) and \(q\) are positive integers. This simplification can be repeated until the integer under the square root sign is not divisible by the square of any integer. The number of tests to determine if \(n = p^2 q\) for some integers \(p\) and \(q\) can be reduced by restricting \(p\) to be prime. The first few squared prime numbers are: \(2^2 = 4\), \(3^2 = 9\), \(5^2 = 25\), \(7^2 = 49\), \(11^2 = 121\), \(13^2 = 169\), \(17^2 = 289\), \(19^2 = 361\)
\[ \begin{aligned} \sqrt{90} &= \sqrt{{3}^2 \cdot 10} \\ &= 3 \sqrt{10} \end{aligned} \]