Question

Rewrite each number in the simplest radical form.

√7/√3

√80

−3√32 − √162

Answer 1

Answer:

(i) $\frac{\sqrt{21}}{3}$

(ii) $4\sqrt{5}$

(III) $-21\sqrt{2}$

Part 1 Step-by-step explanation:

We will simplify this expression by multiplying the fraction by the $\frac{\sqrt{3}}\sqrt{3}$. This calculation is shown below,

$\frac{\sqrt{7}}{\sqrt{3}} =\frac{\sqrt{7}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{7\times 3}}{3} =\frac{\sqrt{21}}{3}$

Part 2 Step-by-step explanation:

We will simplify this expression by writing 80 as a product of 16 and 5 and then separating the square roots of this 2 factors and simplifying. This calculation is shown below,

$\sqrt{80}=\sqrt{16\times 5}=\sqrt{16}\times\sqrt{5}=4\sqrt{5}$

Part 3 Step-by-step explanation:

Step 1

Choose the first term to simply first $-3\sqrt{32}$.

Step 2

Simplify the first term by first factoring 32 as the product of 2 and 16 simplifying by separating the square roots and simplifying. This is shown in the calculation below,

$-3\sqrt{32}=-3\sqrt{2\times 16}=-3\sqrt{2}\times \sqrt{16} =-3\sqrt{2}\times 4=-12\sqrt{2}$

Step 3

In this step we simplify the second term of the expression $-\sqrt{162}$

Step 4

We start the process by factoring 162 as a product of 2 and 81. We then proceed by separating the square roots and simplifying the radicals.

$-\sqrt{162}=-\sqrt{2\times81}=-\sqrt{2}\times9=-9\sqrt{2}$

Step 5

The next step is to combine these simplified terms and add them. This calculation is shown below,

$-12\sqrt{2}-9\sqrt{2}=-21\sqrt{2}$