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For Which Value of P and W is P+W a rational number. Tell me how you got that answer

1) P= 1/ square root of 3 and W=1/square root of 6

2)P=1/ square root of 4 and W=1/square root of 9

3)P=1/square root of 6 and W=1/square root of 10

4)P=1/square root of 25 and W=1/square root of 2

Verified Answer :

300.02 if you use the square root of 72

Answer:

Option 2 - P=1/ square root of 4 and W=1/square root of 9                                  

Step-by-step explanation:

To find : For Which Value of P and W is P+W a rational number ?

Solution :

Solving each expression,

1) P= 1/ square root of 3 and W=1/square root of 6

i.e. \(P=\frac{1}{\sqrt{3}}\) and \(W=\frac{1}{\sqrt{6}}\)

\(P+W=\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{6}}\)

\(P+W=\frac{\sqrt2+1}{\sqrt{6}}\)

\(P+W=0.985598559...\)

It is an irrational number.

2) P=1/ square root of 4 and W=1/square root of 9

i.e. \(P=\frac{1}{\sqrt{4}}\) and \(W=\frac{1}{\sqrt{9}}\)

\(P+W=\frac{1}{\sqrt{4}}+\frac{1}{\sqrt{9}}\)

\(P+W=\frac{1}{2}+\frac{1}{3}\)

\(P+W=\frac{5}{6}\)

\(P+W=0.833333.....\)

It is a rational number as repeating decimal.

3) P=1/square root of 6 and W=1/square root of 10

i.e. \(P=\frac{1}{\sqrt{6}}\) and \(W=\frac{1}{\sqrt{10}}\)

\(P+W=\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{10}}\)

\(P+W=\frac{\sqrt5+\sqrt3}{\sqrt{30}}\)

\(P+W=0.724476056.....\)

It is an irrational number.

4) P=1/square root of 25 and W=1/square root of 2

i.e. \(P=\frac{1}{\sqrt{25}}\) and \(W=\frac{1}{\sqrt{2}}\)

\(P+W=\frac{1}{5}+\frac{1}{\sqrt{2}}\)

\(P+W=\frac{\sqrt2+5}{5\sqrt{2}}\)

\(P+W=0.9071067811.....\)

It is an irrational number.

Therefore, Option 2 is correct.

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