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16 Sep 2014, 00:11
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Which of the following equals to \(\sqrt{36+64+5^2} + \sqrt{20}\)?
A. \(19 + \sqrt{20}\)
B. \(19\sqrt{20}\)
C. \(\sqrt{145}\)
D. \(5\sqrt{100}+\sqrt{20}\)
E. \(7\sqrt{5}\)
A. \(19 + \sqrt{20}\)
B. \(19\sqrt{20}\)
C. \(\sqrt{145}\)
D. \(5\sqrt{100}+\sqrt{20}\)
E. \(7\sqrt{5}\)
16 Sep 2014, 00:11
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Official Solution:
Which of the following equals to \(\sqrt{36+64+5^2} + \sqrt{20}\)?
A. \(19 + \sqrt{20}\)
B. \(19\sqrt{20}\)
C. \(\sqrt{145}\)
D. \(5\sqrt{100}+\sqrt{20}\)
E. \(7\sqrt{5}\)
\(\sqrt{36+64+5^2} + \sqrt{20} = \)
\(=\sqrt{125} + \sqrt{20} = \)
\(=\sqrt{25*5} + \sqrt{4*5} = \)
\(=5\sqrt{5} + 2\sqrt{5} = \)
\(=7\sqrt{5}\).
Answer: E
Which of the following equals to \(\sqrt{36+64+5^2} + \sqrt{20}\)?
A. \(19 + \sqrt{20}\)
B. \(19\sqrt{20}\)
C. \(\sqrt{145}\)
D. \(5\sqrt{100}+\sqrt{20}\)
E. \(7\sqrt{5}\)
\(\sqrt{36+64+5^2} + \sqrt{20} = \)
\(=\sqrt{125} + \sqrt{20} = \)
\(=\sqrt{25*5} + \sqrt{4*5} = \)
\(=5\sqrt{5} + 2\sqrt{5} = \)
\(=7\sqrt{5}\).
Answer: E
22 Jul 2016, 01:58
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Lengthier way of solving this without applying brain - did take only 1.30 minutes to solve though.
This is an appromixation question and answer has to be selected by elimination without carrying out actual calculations.
\(\sqrt{125}\) + \(\sqrt{20}\). Now square root of 125 would be higher than 11 (121) and lower than 12 (144) and square root of 20 would be higher than 4 (16) and lower than 5 (25) so the total sum would be higher than 15 (11+4) but lower than 17 (12+5). Now let's go to the options one by one :-
a) 19 + \(\sqrt{20}\) - higher than 19 - eliminated
b) 19\(\sqrt{20}\) - higher than 19 - eliminated
c) \(\sqrt{145}\) - higher than 12 (144) but lower than 13 (169) - eliminated
d) 5\(\sqrt{100}\) + \(\sqrt{20}\) = 5*10 + \(\sqrt{20}\) - higher than 50 - eliminated
e) 7[m]\sqrt{5} = 7 * 2.23 ( you are not required to know exact value even 2.xx will do - only option which is closer to the estimated values of 15 - 17. Actual Value 2.236
This is an appromixation question and answer has to be selected by elimination without carrying out actual calculations.
\(\sqrt{125}\) + \(\sqrt{20}\). Now square root of 125 would be higher than 11 (121) and lower than 12 (144) and square root of 20 would be higher than 4 (16) and lower than 5 (25) so the total sum would be higher than 15 (11+4) but lower than 17 (12+5). Now let's go to the options one by one :-
a) 19 + \(\sqrt{20}\) - higher than 19 - eliminated
b) 19\(\sqrt{20}\) - higher than 19 - eliminated
c) \(\sqrt{145}\) - higher than 12 (144) but lower than 13 (169) - eliminated
d) 5\(\sqrt{100}\) + \(\sqrt{20}\) = 5*10 + \(\sqrt{20}\) - higher than 50 - eliminated
e) 7[m]\sqrt{5} = 7 * 2.23 ( you are not required to know exact value even 2.xx will do - only option which is closer to the estimated values of 15 - 17. Actual Value 2.236
