How do you evaluate 3 + sqrt(x+7) - sqrt(3x) when x = 9?

3 Answers
May 10, 2018

=>7-3sqrt(3)

Explanation:

3+ sqrt(x+7) - sqrt(3x)

When x = 9, we get

3+sqrt(9+7) - sqrt(3*9)

=3+sqrt(16) - sqrt(3*3^2)

=3+4 - 3sqrt(3)

=7-3sqrt(3)

May 10, 2018

7-3 * (3)^(1/2)

Explanation:

Put 9 in place of x

3+(9+7)^(1/2) -(3*9)^(1/2)

It will be

3+16^(1/2) -27^(1/2)

As

16^(1/2)=4

Thus

3+4-27^(1/2)

It will be

7-27^(1/2)

As 27^(1/2) can be simplified to (3*9)^(1/2) and as 3*9=27, it will be the same as

3^(1/2) * 9^(1/2)

Since

9^(1/2) =3

It will be

3^(1/2) * 3

Coming back to

7-27^(1/2)

As

27^(1/2) = 3 * 3^(1/2)

So it will be

7-3 * 3^(1/2)

May 10, 2018

=>7-3sqrt3

Explanation:

Plugging in 9 for x, we get

3+sqrt(9+7)-sqrt(3*9)

which simplifies to

3+sqrt(16)-sqrt(27)

sqrt16 evaluates to 4. Thus we have

3+4-sqrt(27)

=>7-sqrt(27)

We can rewrite sqrt27 as sqrt(9)*sqrt3. We get

7-(sqrt9*sqrt3)

=>7-3sqrt3

Hope this helps!