Question

station 5
evaluate the expressions.

1. \\(\sqrt{75} - \sqrt{12}\\)
2. \\(\sqrt{72} + 3\sqrt{2}\\)

Explanation:

Problem 13: $\boldsymbol{\sqrt{75} - \sqrt{12}}$

Step1: Simplify each square root

Simplify $\sqrt{75}$: $75 = 25 \times 3$, so $\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$.
Simplify $\sqrt{12}$: $12 = 4 \times 3$, so $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$.

Step2: Subtract the simplified radicals

Substitute the simplified forms into the expression: $5\sqrt{3} - 2\sqrt{3} = (5 - 2)\sqrt{3} = 3\sqrt{3}$.

Problem 14: $\boldsymbol{\sqrt{72} + 3\sqrt{2}}$

Step1: Simplify the square root

Simplify $\sqrt{72}$: $72 = 36 \times 2$, so $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$.

Step2: Add the simplified radicals

Substitute the simplified form into the expression: $6\sqrt{2} + 3\sqrt{2} = (6 + 3)\sqrt{2} = 9\sqrt{2}$.

Answer:

s:

1. $\boldsymbol{3\sqrt{3}}$
2. $\boldsymbol{9\sqrt{2}}$