Question

simplify root54+ root175​

Answer 1

Answer:

Step-by-step explanation:

First, simplify each square root:

√

175

, is  

175

divisible by a perfect square (other than 1)?

We could go through the list starting with  

2

2

=

4

is not a factor and  

3

2

=

9

is not a factor, and when we get to  

5

2

=

25

, we find that:

175

=

25

×

7

So  

√

175

=

√

25

×

7

=

√

25

×

√

7

=

5

√

7

.

We cannot further simplfy  

√

7

so we'll simplify the other square root.

28

=

4

×

7

, so we get:

√

28

=

√

4

×

7

=

2

√

7

Here's the short way to write what we've done:

√

175

−

√

28

=

√

25

×

7

−

√

4

×

7

=

5

√

7

−

2

√

7

Now, if we have 5 of these things and we subtract 2 of the things, surely we end up with 3 of the things.

So:

√

175

−

√

28

=

5

√

7

−

2

√

7

=

3

√

7

Answer 2

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