Practicing the Intermediate 2nd Year Maths 2A Textbook Solutions Inter 2nd Year Maths 2A Binomial Theorem Solutions Exercise 6(c) will help students to clear their doubts quickly.

## Intermediate 2nd Year Maths 2A Binomial Theorem Solutions Exercise 6(c)

Question 1.

Find an approximate value of the following corrected to 4 decimal places.

(i) \(\sqrt[5]{242}\)

Solution:

(ii) \(\sqrt[7]{127}\)

Solution:

(iii) \(\sqrt[5]{32.16}\)

Solution:

(iv) \(\sqrt{199}\)

Solution:

(v) \(\sqrt[3]{1002}-\sqrt[3]{998}\)

Solution:

(vi) \((1.02)^{3 / 2}-(0.98)^{3 / 2}\)

Solution:

Question 2.

If |x| is so small that x^{2} and higher powers of x may be neglected then find the approximate values of the following.

(i) \(\frac{(4+3 x)^{1 / 2}}{(3-2 x)^2}\)

Solution:

(ii) \(\frac{\left(1-\frac{2 x}{3}\right)^{3 / 2}(32+5 x)^{1 / 5}}{(3-x)^3}\)

Solution:

(iii) \(\sqrt{4-x}\left(3-\frac{x}{2}\right)^{-1}\)

Solution:

(iv) \(\frac{\sqrt{4+x}+\sqrt[3]{8+x}}{(1+2 x)+(1-2 x)^{-1 / 3}}\)

Solution:

(v) \(\frac{(8+3 x)^{2 / 3}}{(2+3 x) \sqrt{4-5 x}}\)

Solution:

Question 3.

Suppose s and t are positive and t is very small when compared to s. Then find an approximate value of \(\left(\frac{s}{s+t}\right)^{1 / 3}-\left(\frac{s}{s-t}\right)^{1 / 3}\)

Solution:

Since t is very small when compared with s, \(\frac{t}{s}\) is very very small.

Question 4.

Suppose p, q are positive and p is very small when compared to q. Then find an approximate value of \(\left(\frac{q}{q+p}\right)^{1 / 2}+\left(\frac{q}{q-p}\right)^{1 / 2}\)

Solution:

Question 5.

By neglecting x^{4} and higher powers of x, find an approximate value of \(\sqrt[3]{x^2+64}-\sqrt[3]{x^2+27}\)

Solution:

Question 6.

Expand 3√3 in increasing powers of \(\frac{2}{3}\).

Solution: