sqr root * exponents

[mikeclarke44]

I seem to be close on this one but something in my math seems off.

Of the following integers which is the closest approx to (sqr root 2 + sqr root 5)^2

a) 7
b) 10
c) 13
d) 15
e) 17

I get (SR 2 + SR 5)(SR 2 + SR 5)
2 + SR10 + SR10 + 5
7 + SR20
7 + SR4 + SR 5
9 + SR5
Which probabily 11+ a little bit more. The answer is (c), but is my math right?

[Neo2000]

I seem to be close on this one but something in my math seems off.

I get (SR 2 + SR 5)(SR 2 + SR 5)
2 + SR10 + SR10 + 5
7 + SR20
7 + SR4 + SR 5
9 + SR5
Which probabily 11+ a little bit more. The answer is (c), but is my math right?

SR10 + SR10 = 2SR10 = SR40

[mikeclarke44]

Still not following you.
I understand that SR10 + SR10 = 2SR10
but you lost me when you said 2SR10 = SR40

[thumpin_termis]

but you lost me when you said 2SR10 = SR40

2SR10 = SR(4*10) = SR40

If don't get that, then check this link out and review working with square roots.
https://www.purplemath.com/modules/radicals.htm

[mikeclarke44]

Thanks, that does help!

[moneyman]

(Sq.root 2+Sq.root5)^2 is in the format of (a+b)^2

(a+b)^2 is a^2+2ab+b^2

Substitute the values in the formula and you will get

(Sq.rt 2)^2+2(Sq.rt2)(Sq.rt5)+(Sq.rt5)^2

The result is 2+2(Sq.rt 10)+5 which is 7+2(sq.rt10)

Sq.rt 9 is 3 ,so sq.rt 10 should be somewhere around 3.1 or 3.2 and so

7+2(3.1) would be close to answer choice C

[vmahalin]

This is how it goes,

(sq2 + sq5)^2 = (sq2)^2 + (sq5)^2 + 2 x (sq2) x (sq5)

[apply formula (a+b)^2]

= 2 + 5 + 2(sq 10)

Now the question is "value closest to", instead of sq10 assume sq9.
sq9 is 3.

= 7 + 2(sq9) = 7 + (2 x 3) = 13.

Hence the answer is 13.

[jaspetrovic]

I agree w/C.