Question

Simplify: √27 + √3

Answer 1

Start by simplifying \(\sqrt{27} \)
Can you find two factors of 27, one of which being a perfect square?

Answer 2

so the square root of 30? which would be 10 outside the square root of 3?

Answer 3

Just like in the previous problem, \(\sqrt{48} \), 48 = 16 * 3, and 16 is a perfect square, you can rewrite 27 as the product of two numbers, one of them being a perfect square.

Answer 4

10√3 so would this be the answer???

Answer 5

No. There is no 30 here.
Start with 27.
Can you think of two numbers that multiply to 27 from the multiplication tables?

Answer 6

9 and 3

Answer 7

Great.
Now what about 9? Is it a perfect square?
Is 9 the square of some number?

Answer 8

3 and 3

Answer 9

Exactly. 9 is 3 * 3, or 3^2.
Now we can continue with the problem:

\(\sqrt{27} + \sqrt 3=\)

\(= \sqrt{9 \times 3} + \sqrt 3\)

So far we are only showing that 27 = 9 * 3

Ok?

Answer 10

ok

Answer 11

Now we can separate the numbers inside the root.

\(= \sqrt{9} \times \sqrt 3 + \sqrt 3\)

In the step above, all we did was to separate the root of the product 9 * 3 into the product of the roots of 9 and 3.

Answer 12

yep i see so far.

Answer 13

Now we can easily simplify \(\sqrt 9\)
We know that \(\sqrt 9 = 3\), so we write 3 instead of \(\sqrt 9\):

\(= 3\sqrt 3 + \sqrt 3\)

On the left above you see how \(\sqrt {27} \) simplifies to \(3 \sqrt 3\)

Answer 14

Now we need to do the addition.

\(3\sqrt 3 + \sqrt 3\)

Is the same as saying "what is 3 square roots of 3 added to 1 square roots of three?"

Answer 15

i understand. but what answer is it?

Answer 16

A. 10√3
B. 27
C. 9√3
D. 4√3

Answer 17

What is 3x + x?
What is 3 oranges plus 1 orange?

Answer 18

4 oranges

Answer 19

What is 3 of something plus one of the same thing?

Answer 20

4

Answer 21

Right, so the same way 3 square roots of 3 added to 1 square root of 3 is 4 square roots of 3.
Now we can finish the problem.

\(= 4 \sqrt 3\)

Answer 22

oh that makes a lot more sense

Answer 23

Here is the whole problem without the explanations in the middle:

\(\sqrt{27} + \sqrt 3=\)

\(= \sqrt{ 9 \times 3} + \sqrt 3\)

\(=\sqrt 9 \times \sqrt 3 + \sqrt 3\)

\(= 3\sqrt 3 + \sqrt 3\)

\(= 4 \sqrt 3\)

Answer 24

thank you! cane help me with another?

Answer 25

Multiply and simplify: square root of 6 times the quantity of square root of 3 + 5 square root of 2.
A.
B.
C.

Answer 26

You mean this?

\(\sqrt 6 \times (\sqrt 3 + 5 \sqrt 2) \)