Question

what is the positive square root of 8,100?

Explanation:

Step1: Recall square - root definition

The square root of a number \(x\) is a value \(y\) such that \(y^2=x\). We want the positive square root of \(8100\).

Step2: Factorize 8100

We know that \(8100 = 81\times100\).

Step3: Find square roots of factors

The square root of \(81\) is \(9\) (\(\sqrt{81}=9\)) and the square root of \(100\) is \(10\) (\(\sqrt{100} = 10\)).

Step4: Calculate square root of 8100

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 81\), \(b = 100\)), we have \(\sqrt{8100}=\sqrt{81}\times\sqrt{100}=9\times10 = 90\).

Answer:

90