Operations on Rational and Irrational Numbers

Q.

Using appropriate properties find:$\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Q.

Give an example of each, of two irrational numbers whose:

(i) difference is a rational number.

(ii) difference is an irrational number.

(iii) sum is a rational number.

(iv) sum is an irrational number.

(v) product is a rational number.

(vi) product is an irrational number.

(vii) quotient is a rational number.

(viii) quotient is an irrational number.

Q.

How do you simplify ${\left(125\right)}^{-\frac{1}{3}}$?

Q.

What are three irrational numbers between $2$and $3$?

Q.

Prove √6 as an irrational number

Q.

Evaluate $\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}$, it us given that $\sqrt{5}=2.236$ and $\sqrt{10}=3.162$

Q.

The value of $0.\overline{23}$ + $0.\overline{22}$ is

1. $0.\overline{45}$

2. $0.\overline{43}$

3. 0.45

4. $0.\overline{45}$

Q.

If $\sqrt{2}=1.414then\sqrt{\frac{(\sqrt{2}-1)}{(\sqrt{2}+1)}}=?$

(a) 0.207 (b) 2.414 (c) 0.414 (d) 0.621

Q.

All non-terminating and non-recurring decimal numbers are rational numbers.

1. True

2. False

Q.

Which one of the following is an irrational number:

1. $\surd 4$

2. $3\surd 8$

3. $\surd 100$

4. $-\surd 0.64$

Q. 2π is a rational or irrational number?

Q.

Is the product of a rational and irrational number always irrational? Give an example.

Q. Prove that ✓10 is irrational.

Q.

Let a be a rational number and b be an irrational number. Is ab necessarily an irrational number ? Justify your answer with an example.

Q.

Given, $\sqrt{2}=1.4141and\sqrt{6}=2.449,findthevalueof\frac{1}{\sqrt{3}-\sqrt{2}-1}$ correct to 3 places of decimal.

Q.

What Type of Software Is Ms – Word?

Q.

Let $x$ be a rational number and $y$ be an irrational number. Is $x+y$ necessarily an irrational number ? Give an example in support of your answer.

Q. Express $0.4\overline{7}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Q.

Rationalize

1÷√7+√6-√13

Q.

Which is greater: $\left(\frac{1}{2}\right)\text{of}\left(\frac{6}{7}\right)or\left(\frac{2}{3}\right)\text{of}\left(\frac{3}{7}\right)$

Q.

Write a pair of irrational numbers whose product is rational.

Q.

If $x=\frac{\sqrt{3}+1}{2}$, find the value of $4x^3+2x^2-8x+7$.

Q.

Prove that √5-√3is not a rational number

Q.

What is the value of $\frac{16\sqrt{13}}{9\sqrt{52}}$ ?

1. $\frac{3}{9}$

2. $\frac{9}{8}$

3. $\frac{7}{9}$

4. $\frac{8}{9}$

Q.

The value of $\sqrt{5+2\sqrt{6}}$ is

(a)$\sqrt{5}+\sqrt{6}$ (b)$\sqrt{5}-\sqrt{6}$ (c)$\sqrt{3}+\sqrt{2}$ (d)$\sqrt{3}-\sqrt{2}$

Q.

Find the value of $\frac{21\sqrt{12}}{10\sqrt{27}}$

Q.

Simplify the following expressions :

(i) $(4+\sqrt{7})(3+\sqrt{2})$

(ii) $(3+\sqrt{3})(5-\sqrt{2})$

(iii) $(\sqrt{5}-2)(\sqrt{3}-\sqrt{5})$

Q.

$\sqrt{10}\times \sqrt{15}=?$

(a)$\sqrt{25}$ (b)$5\sqrt{6}$ (c)$6\sqrt{5}$ (d) None of these

Q.

When $15\sqrt{15}$is divided by $3\sqrt{3}$ the quotient is

(a)$5\sqrt{3}$

(b)$3\sqrt{5}$

(c)$5\sqrt{5}$

(d)$33$

Q.

Evaluate$\sin 45°+\cos 45°$