Answer:
\(a=2\sqrt5, b= 3\sqrt5\)
Step-by-step explanation:
We are given that tow whole number a and b
ab=30
a:b=2:3
We have to find a and b.
\(ab=30\)
\(\frac{a}{b}=\frac{2}{3}\)
\(a=\frac{2}{3}b\)
Substitute the value of a
\(\frac{2}{3}b\times b=30\)
\(\frac{2}{3}b^2=30\)
\(b^2=\frac{30\times 3}{2}=45\)
\(b=\sqrt{45}=\sqrt{3\times 3\times 5}=\pm3\sqrt5\)
We take the value of positive because b is a whole number
Substitute the value of \(b=3\sqrt 5\)
\(a=\frac{2}{3}\times 3\sqrt5=2\sqrt5\)
Hence, \(a=2\sqrt5, b= 3\sqrt5\)
