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?

mikeclarke44 wrote: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

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

mikeclarke44 wrote: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

(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

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.

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sqr root * exponents

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