# Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.5

Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.5 Textbook Questions and Answers.

## BSEB Bihar Board Class 9th Maths Solutions Chapter 1 Number Systems Ex 1.5

Question 1.
Classify the following numbers as rational or irrational :
(i) 2 – $$\sqrt{5}$$
(ii) (3 + $$\sqrt{23}$$) – $$\sqrt{23}$$
(iii) $$\frac{2 \sqrt{7}}{7 \sqrt{7}}$$
(iv) $$\frac{1}{\sqrt{2}}$$
(v) 2π
Solution:
(i) 2 – $$\sqrt{5}$$ is an irrational number being a difference between a rational and an irrational.
(ii) (3 + $$\sqrt{23}$$) – $$\sqrt{23}$$ = 3 + $$\sqrt{23}$$ – $$\sqrt{23}$$ = 3, which is a rational number.
(iii) $$\frac{2 \sqrt{7}}{7 \sqrt{7}}$$ = $$\frac { 2 }{ 7 }$$, which is a rational number.
(iv) $$\frac{1}{\sqrt{2}}$$ is irrational being the quotient of a rational and an irrational.
(v) 2π is irrational being the product of rational and irrational.

Question 2.
Simplify each of the following expressions :
(i) (3 + $$\sqrt{3}$$)(2 +$$\sqrt{2}$$)
(ii) (3 + $$\sqrt{3}$$(3 – $$\sqrt{3}$$)
(iii) ($$\sqrt{5}$$ + $$\sqrt{2}$$)²
(iv) ($$\sqrt{5}$$ – $$\sqrt{2}$$)($$\sqrt{5}$$ + $$\sqrt{2}$$)
Solution:

Question 3.
Recall, it is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is π = $$\frac { c }{ d }$$. This seems to contradict the fact that n is a irrational. How will you resolve this contradiction?
Solution:
There is no contradiction as either c or d irrational and hence π is an irrational number.

Question 4.
Represent $$\sqrt{9.3}$$ on the number line.
Solution:
Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B, mark a distance of 1 unit and mark the new point as C. Find the mid-point of AC and mark that point as O. Draw a semi-circle with centre O and radius OC. Draw a line perpendicular to AC passing through B and intersecting the semi circle at D.

Then BD = $$\sqrt{9.3}$$ . To represent $$\sqrt{9.3}$$ On the number line. Let us treat the line BC as the number line, with B as zero, C as 1, and so on. Draw an arc with centre B and radius BD, which intersects the number line in E. Then, E represent $$\sqrt{9.3}$$.

Question 5.
Rationalise the denominators of the following :
(i) $$\frac{1}{\sqrt{7}}$$
(ii) $$\frac{1}{\sqrt{7}-\sqrt{6}}$$
(iii) $$\frac{1}{\sqrt{5}+\sqrt{2}}$$
(iv) $$\frac{1}{\sqrt{7}-2}$$
Solution: