sqrt 72 + sqrt 18

6sqrt7 - 4sqrt7

Multiply & express in simplest form
sqrt5 x sqrt20

1/3sqrt18 x sqrt16

Divide & express in simplest form
sqrt80 / sqrt5

sqrt150 / sqrt3

Rationalize the denominator
5
/
2-sqrt3

6
/
sqrt7+2

3
/
sqrt6

2+sqrt3
/
4-sqrt3

## I will do the first one and the last one, you do the rest.

sqrt 72 + sqrt 18
=
sqrt (18*4) + sqrt 18
=
2 sqrt 18 + 1 sqrt 18
=
3 sqrt (3*3*2)
=
9 sqrt 2
-----------------------------
(2+sqrt 3) (4+sqrt3)
/
(4-sqrt 3) (4+sqrt3)
=
(8 +6sqrt 3 + 3 )
/
(16-3)
=
(11 +6 sqrt 3)
/
13

## is there a way that the 1/3sqrt18 x sqrt16 problem can be solved

150 / 3

and
6
sqrt7 + 2

i'm having trouble with those.

## If you mean (1/3)sqrt18 x sqrt16, that is (1/3)sqrt(9*2)* 4 = 4 sqrt 2

Surely you know what 150/3 is.

1. Simplify the numbers inside the radicals as much as possible.
2. Identify if there are any like terms (square roots with the same radicand) that can be combined together.
3. Add or subtract the like terms to get the final answer.

For the question "sqrt 72 + sqrt 18":
1. Simplify the numbers first: sqrt 72 can be further simplified to 6sqrt 2, and sqrt 18 can be further simplified to 3sqrt 2.
2. Since both terms have the same radicand (sqrt 2), you can combine them together.
3. The final answer is 6sqrt 2 + 3sqrt 2 = 9sqrt 2.

For the question "6sqrt7 - 4sqrt7":
1. Both terms already have the same radicand (sqrt 7), so you can subtract them directly.
2. The answer is 6sqrt 7 - 4sqrt 7 = 2sqrt 7.

To multiply and express in simplest form with radicals, you can follow these steps:

1. Multiply the numbers outside of the radicals if any.
2. Multiply the numbers inside the radical.
3. Simplify the resulting number by factoring out perfect square factors.
4. Combine the numbers inside the radical if they have the same radicand.

For the question "sqrt 5 x sqrt 20":
1. There are no numbers outside of the radicals, so you can move to step 2.
2. Multiply the numbers inside the radical: sqrt 5 x sqrt 20 = sqrt (5 x 20) = sqrt 100 = 10.

For the question "1/3 sqrt 18 x sqrt 16":
1. Multiply the numbers outside of the radicals: 1/3.
2. Multiply the numbers inside the radicals: sqrt 18 x sqrt 16 = sqrt (18 x 16) = sqrt 288.
3. Simplify the result: sqrt 288 = sqrt (144 x 2) = sqrt 144 x sqrt 2 = 12sqrt 2.
4. Multiply the numbers outside the radicals with the simplified result: (1/3) x 12sqrt 2 = 4sqrt 2.

To divide and express in simplest form with radicals, you can follow these steps:

1. Divide the numbers outside of the radicals if any.
2. Divide the numbers inside the radicals.
3. Simplify the resulting number by factoring out perfect square factors.
4. Combine the numbers inside the radical if they have the same radicand.

For the question "sqrt 80 / sqrt 5":
1. Divide the numbers outside of the radicals: sqrt 80 / sqrt 5 = sqrt (80/5) = sqrt 16 = 4.

For the question "sqrt 150 / sqrt 3":
1. Divide the numbers outside of the radicals: sqrt 150 / sqrt 3 = sqrt (150/3) = sqrt 50 = 5.

To rationalize the denominator, you can follow these steps:

1. Multiply both the numerator and denominator by the conjugate of the denominator.
2. Simplify the result by expanding and combining like terms.
3. Simplify the radicals if possible.

For the question "5 / (2 - sqrt 3)":
1. Multiply the numerator and denominator by the conjugate of the denominator, which is (2 + sqrt 3).
2. Simplify the result: 5 * (2 + sqrt 3) = 10 + 5sqrt 3.
3. Since there are no more radicals in the denominator, the expression is already rationalized.

For the question "6 / (sqrt 7 + 2)":
1. Multiply the numerator and denominator by the conjugate of the denominator, which is (sqrt 7 - 2).
2. Simplify the result: 6 * (sqrt 7 - 2) = 6sqrt 7 - 12.
3. The denominator no longer has a radical, so the expression is already rationalized.

For the question "3 / sqrt 6":
1. Multiply the numerator and denominator by the conjugate of the denominator, which is sqrt 6.
2. Simplify the result by expanding: 3 * sqrt 6 = 3sqrt 6.
3. The denominator no longer has a radical, so the expression is already rationalized.

For the question "(2 + sqrt 3) / (4 - sqrt 3)":
1. Multiply the numerator and denominator by the conjugate of the denominator, which is (4 + sqrt 3).
2. Simplify the result by expanding and combining like terms: (2 + sqrt 3) * (4 + sqrt 3) = 8 + 6sqrt 3 + 3 = 11 + 6sqrt 3.
3. The denominator no longer has a radical, so the expression is already rationalized.