How do you simplify $\sqrt{45}$ $sqrt(45)$ ?

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Answer 1 · 2018-03-03T14:01:15

$\sqrt{45} = 3 \sqrt{5}$ $sqrt(45) = 3sqrt(5)$

We must use our knowledge of surds:

$\sqrt{a \cdot b \cdot c} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$ $sqrt(a*b*c) = sqrt(a)*sqrt(b)*sqrt(c)$

We know $45 = 3 \cdot 3 \cdot 5$ $45 = 3*3*5$

$\Rightarrow \sqrt{45} = \sqrt{3 \cdot 3 \cdot 5} = \sqrt{3} \cdot \sqrt{3} \cdot \sqrt{5}$ $=> sqrt(45) = sqrt(3*3*5) = sqrt(3)*sqrt(3)*sqrt(5)$

We know $\sqrt{a} \cdot \sqrt{a} = a$ $sqrt(a) * sqrt(a) = a$

$\Rightarrow \sqrt{3} \cdot \sqrt{3} \cdot \sqrt{5} = 3 \cdot \sqrt{5}$ $=> sqrt(3)*sqrt(3)*sqrt(5) = color(red)(3 *sqrt(5)$

How do you simplify √45sqrt(45)?