Question

1. \\(sqrt{28}\\)\
2. \\(sqrt{450}\\)\

use the perfect cube numbers below to break the problem apart:

Explanation:

Problem 11: Simplify $\boldsymbol{\sqrt{28}}$

Step1: Factor 28 into perfect square and other

We know that \(28 = 4\times7\), where \(4\) is a perfect square (\(4 = 2^2\)). So we can rewrite \(\sqrt{28}\) as \(\sqrt{4\times7}\).

Step2: Use square root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we get \(\sqrt{4\times7}=\sqrt{4}\times\sqrt{7}\).

Step3: Simplify \(\sqrt{4}\)

Since \(\sqrt{4} = 2\), we substitute it back to get \(2\sqrt{7}\).

Step1: Factor 450 into perfect square and other

We factor \(450\) as \(225\times2\), where \(225\) is a perfect square (\(225 = 15^2\)). So \(\sqrt{450}=\sqrt{225\times2}\).

Step2: Use square root property

Using \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\)), we have \(\sqrt{225\times2}=\sqrt{225}\times\sqrt{2}\).

Step3: Simplify \(\sqrt{225}\)

Since \(\sqrt{225}=15\), we substitute it back to get \(15\sqrt{2}\).

Answer:

\(2\sqrt{7}\)

Problem 12: Simplify $\boldsymbol{\sqrt{450}}$