Daily Practice Problems

Class 9 Maths

Number Systems

Class 9 Maths

Number Systems

**Question 1:**

Simplify: (√5 + √2)^{2}

**Question 2:**

Identify a rational number among the following numbers:

2 + √2, 2√2, 0 and π

**Question 3:**

Express 23.43 in form, where p, q are integers and q ≠ 0.

**Question 4:**

Simplify: √45 – 3√20 + 4√5

**Question 5:**

Rationalize the denominator of the following:

(i) (ii)

**Question 6:**

If x + = √3, find value of x^{3} + .

**Question 7:**

Represent √17 on number line.

**Question 8:**

If = a + b√6, the find the value of a and b.

**Question 9:**

Represent √5 on number line.

**Question 10:**

Find out three rational numbers lying between 3 and 4.

**Question 11:**

If 7^{2x + 3} = 1, then what is the value of x?

**Question 12:**

Convert 0.4777777.... in form.

**Question 13:**

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

**Question 14:**

Visualize 3.765 on the number line, using successive magnification.

**Question 15:**

Simplify: (i) * (ii) (iii)

**Question 16:**

What is the product of a rational and an irrational number?

(a) Always an integer

(b) Always a rational number

(c) Always an irrational number

(d) Sometimes rational and sometimes irrational

**Question 17:**

How many rational numbers and irrational numbers can be inserted between 4 and 5?

**Question 18:**

Write the following in decimal form and say what kind of decimal expansion each has:

(i) (ii) (iii)

**Question 19:**

Find the value of when √10 = 3.162.

**Question 20:**

If x = , find the value of x^{2} – 4x – 1.

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