Question

extension
use mental math to evaluate each expression.

1. \\(\sqrt{5} + \sqrt{2} \cdot \sqrt{8} - \sqrt{5}\\)
2. \\(\sqrt{6} \cdot \sqrt{6} + 2\sqrt{3} \cdot 2\sqrt{3}\\)

Explanation:

Problem 1

Step1: Simplify the product of square roots

Recall that \(\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}\). So, \(\sqrt{2}\cdot\sqrt{8}=\sqrt{2\times8}=\sqrt{16}\)

Step2: Evaluate the square root and simplify the expression

\(\sqrt{16} = 4\). Now the expression becomes \(\sqrt{5}+4 - \sqrt{5}\)

Step3: Combine like terms

\(\sqrt{5}-\sqrt{5}=0\), so \(0 + 4=4\)

Step1: Simplify each product of square roots

For \(\sqrt{6}\cdot\sqrt{6}\), using \(\sqrt{a}\cdot\sqrt{a}=a\), we get \(6\). For \(2\sqrt{3}\cdot2\sqrt{3}\), first multiply the coefficients \(2\times2 = 4\) and then \(\sqrt{3}\cdot\sqrt{3}=3\), so \(4\times3 = 12\)

Step2: Add the results

Now add \(6\) and \(12\): \(6 + 12=18\)

Answer:

\(4\)

Problem 2