How do you simplify $\sqrt{15} \cdot \sqrt{45}$ $sqrt15 * sqrt45$ ?

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Answer 1 · 2016-05-01T15:25:07

$15 \sqrt{3}$ $15sqrt(3)$

Given,

$\sqrt{15} \cdot \sqrt{45}$ $sqrt(15)*sqrt(45)$

Break down each radical using square numbers. Since $\sqrt{15}$ $sqrt(15)$ cannot be simplified any further, it is left as is.

$= \sqrt{15} \cdot \sqrt{9 \cdot 5}$ $=sqrt(15)*sqrt(9*5)$

Since $\sqrt{9} = 3$ $sqrt(9)=3$ , you can simplify the second radical.

$= \sqrt{15} \cdot 3 \sqrt{5}$ $=sqrt(15)*3sqrt(5)$

Now that the second radical is simplified, multiply it by the first radical.

$= 3 \sqrt{15 \cdot 5}$ $=3sqrt(15*5)$

$= 3 \sqrt{75}$ $=3sqrt(75)$

Break down $\sqrt{75}$ $sqrt(75)$ using square numbers.

$= 3 \sqrt{25 \cdot 3}$ $=3sqrt(25*3)$

Since $\sqrt{25} = 5$ $sqrt(25)=5$ , you can simplify the radical.

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

$=color(green)(|bar(ul(color(white)(a/a)color(black)(15sqrt(3))color(white)(a/a)|)))$

How do you simplify sqrt15 * sqrt45√15⋅√45sqrt15 * sqrt45?