Answer:
(i) [tex]\frac{\sqrt{21}}{3}[/tex]
(ii) [tex]4\sqrt{5}[/tex]
(III) [tex]-21\sqrt{2}[/tex]
Part 1 Step-by-step explanation:
We will simplify this expression by multiplying the fraction by the [tex] \frac{\sqrt{3}}\sqrt{3}[/tex]. This calculation is shown below,
[tex]\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}[/tex]
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,
[tex]\sqrt{80}=\sqrt{16\times 5}=\sqrt{16}\times\sqrt{5}=4\sqrt{5}[/tex]
Part 3 Step-by-step explanation:
Step 1
Choose the first term to simply first [tex]-3\sqrt{32}[/tex].
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,
[tex]-3\sqrt{32}=-3\sqrt{2\times 16}=-3\sqrt{2}\times \sqrt{16} =-3\sqrt{2}\times 4=-12\sqrt{2}[/tex]
Step 3
In this step we simplify the second term of the expression [tex]-\sqrt{162}[/tex]
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.
[tex]-\sqrt{162}=-\sqrt{2\times81}=-\sqrt{2}\times9=-9\sqrt{2}[/tex]
Step 5
The next step is to combine these simplified terms and add them. This calculation is shown below,
[tex]-12\sqrt{2}-9\sqrt{2}=-21\sqrt{2}[/tex]
