If x varies directly as square root of y and x = 81 when y = 9, Find x when y = 1\(\frac{7}{9}\)

A.

20\(\frac{1}{4}\)

B.

27

C.

2\(\frac{1}{4}\)

D.

36

Correct answer is D

x \(\alpha\sqrt y\)

x = k\(\sqrt y\)

81 = k\(\sqrt9\)

k = \(\frac{81}{3}\)

= 27

therefore, x = 27\(\sqrt y\)

y = 1\(\frac{7}{9}\) = \(\frac{16}{9}\)

x = 27 x \(\sqrt{\frac{16}{9}}\)

= 27 x \(\frac{4}{3}\)

dividing 27 by 3

= 9 x 4

= 36