5√2 percent of 1/√200 =

I. Arithmetic
Change the denominator either initially* or while solving, as here

Setup: 10 percent of \(\frac{1}{2}=\)
LHS: \((\frac{10}{100}*\frac{1}{2})\)

\(5√2\) percent of \(\frac{1}{√200}\):

\((\frac{5\sqrt{2}}{100}*\frac{1}{\sqrt{200}})=\frac{5\sqrt{2}}{100*\sqrt{200}}=\)

\(\frac{5\sqrt{2}}{100*\sqrt{100*2}}=\)

\(\frac{5\sqrt{2}}{100*10\sqrt{2}}=\)

\(\frac{5}{100*10}=\frac{1}{100*2}=\frac{1}{200}=\)

\(0.005\)

Answer A

II. Approximate in pieces

\(5√2\) percent of \(\frac{1}{√200}\)?

(1) \(5\sqrt{2}\approx{(5*1.4)}\approx{7}\)

\(7\) percent =\(0.07\)

(2) \(\frac{1}{\sqrt{200}}\):
the denominator is between 14 and 15. \(14^2=196\), and \(15^2=225\)

\(\sqrt{196}<\sqrt{200}<\sqrt{225}\)

\(\sqrt{200}\) is closer to 14:
\(\frac{1}{\sqrt{200}}\approx{\frac{1}{14}}\approx{0.07}\)

(3) Together: 7 percent of 0.07 =

\((0.07*0.07)=0.0049\)

\(\approx{0.005}\)

Answer A

*\(\frac{1}{\sqrt{200}}\)
Change the denominator
\(\sqrt{200}=\sqrt{100*2}=10\sqrt{2}=>\)
\(\frac{1}{\sqrt{200}}=\\
\frac{1}{10\sqrt{2}}\)

We can express 5√2 percent as 5√2/100. Thus, we have:

(5√2)/100 x (1/√200) = (5√2)/(100√200) =1/(20 x 10) = 1/200 = 0.005

Answer: A

This is how i solved


5 √ 2/ 100 * 1 /√ 200

5 √ 2/ 5*20 * 1 /√ 100*2

Cancel 5's from top and bottom of LHS

= √2 / 20 * 1 / √100*√2

= √2 /20* 1 / 10*√2

cANCEL ROOT 2 FROM TOP AND BOTTOM

= 1 / 200

= 0r 0.005 ans choice A

5√2/100 * 1/√200

√200 = 10√2

5√2/100 * 1/√200 = 1/200 = 0.005 (A)

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