Question

Rewrite each number in the simplest radical form.

√7/√3

√80

−3√32 − √162

Answer 1

(i)
`(√(21))/(3)`

(ii)
`4√(5)`

(III)
`-21√(2)`

Part 1 Step-by-step explanation:

We will simplify this expression by multiplying the fraction by the
`\frac{√(3)}√(3)`. This calculation is shown below,

`(√(7))/(√(3)) =(√(7))/(√(3)) * (√(3))/(√(3))=(√(7* 3))/(3) =(√(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,

`√(80)=√(16* 5)=√(16)*√(5)=4√(5)`

Part 3 Step-by-step explanation:

Step 1

Choose the first term to simply first
`-3√(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√(32)=-3√(2* 16)=-3√(2)* √(16) =-3√(2)* 4=-12√(2)`

Step 3

In this step we simplify the second term of the expression
`-√(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.

`-√(162)=-√(2*81)=-√(2)*9=-9√(2)`

Step 5

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

`-12√(2)-9√(2)=-21√(2)`