## anonymous one year ago Simplify: √27 + √3

1. mathstudent55

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

2. anonymous

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

3. mathstudent55

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.

4. anonymous

10√3 so would this be the answer???

5. mathstudent55

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

6. anonymous

9 and 3

7. mathstudent55

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

8. anonymous

3 and 3

9. mathstudent55

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?

10. anonymous

ok

11. mathstudent55

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.

12. anonymous

yep i see so far.

13. mathstudent55

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 $$3 \sqrt 3$$

14. mathstudent55

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?"

15. anonymous

i understand. but what answer is it?

16. anonymous

A. 10√3 B. 27 C. 9√3 D. 4√3

17. mathstudent55

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

18. anonymous

4 oranges

19. mathstudent55

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

20. anonymous

4

21. mathstudent55

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. $$= 4 \sqrt 3$$

22. anonymous

oh that makes a lot more sense

23. mathstudent55

Here is the whole problem without the explanations in the middle: $$\sqrt{27} + \sqrt 3=$$ $$= \sqrt{ 9 \times 3} + \sqrt 3$$ $$=\sqrt 9 \times \sqrt 3 + \sqrt 3$$ $$= 3\sqrt 3 + \sqrt 3$$ $$= 4 \sqrt 3$$

24. anonymous

thank you! cane help me with another?

25. anonymous

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

26. mathstudent55

You mean this? $$\sqrt 6 \times (\sqrt 3 + 5 \sqrt 2)$$