Properties of Multiplication of Integers

Q. Evaluate (99)³ by using suitable identity.

Q.

if a= 6+2√3 then Find the value of a-1/a

Q.

Evaluate 98 x 102.

1. 9996

2. 9898

3. 9988

4. 9899

Q. Evaluate each of the following:

(i) 111³ − 89³

(ii) 46³+34³

(iii) 104³ + 96³

(iv) 93³ − 107³

Q. Evaluate:

(i) 25³ − 75³ + 50³

(ii) 48³ − 30³ − 18³

(iii) ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3$

(iv) (0.2)³ − (0.3)³ + (0.1)³

Q.

Question 5(g)
Find the product, using suitable properties:
$(-17)\times (-29)$

Q. If a + b + c = 9 and ab + bc + ca =23, then a³ + b³ + c³ − 3abc =

(a) 108

(b) 207

(c) 669

(d) 729

Q. Rationalize the denominator.

(i) $\frac{1}{\sqrt{5}}$ (ii) $\frac{2}{3\sqrt{7}}$ (iii) $\frac{1}{\sqrt{3}-\sqrt{2}}$ (iv) $\frac{1}{3\sqrt{5}+2\sqrt{2}}$ (v) $\frac{12}{4\sqrt{3}-\sqrt{2}}$

Q.

Question 3(i)
For any integer a, what is $(-1)\times a$ equal to?

Q.

If 'a' and 'b' are any two integers and a × (b + c) = (a × b) + (a × c). The property used here is the ____ property.

Q.

Question 89

State whether the statement is True or False.

Product of three negative integers is a negative integer.

Q.

Evaluate: 5³ - 2³ - 3³

1. 120

2. 60

3. 90

4. -90

Q.

Which of the following expressions is equivalent to the expression 706 × 695?

1. (600)² + 600 − 6 × 5

2. (700)² + 700 − 6 × 5

3. 600² + (95 + 6) 600 − 11

4. 700² + (95 + 6) 700 − 11

Q.

Simplify: 1/(256)1/3 + 1/(256)1/2 + 2/(243)2/3

Prove that : 1/(1+ √2) + 1/(√2+ √3) + 1/(√2+ √3) + 1/(√2+ √3) + 1/(√2+ √3) + 1/(√2+ √3 )

+ 1/(√2+ √3 )+ 1/(√2+ √3) = 2

.Prove that: {81/16}-3/2 x [ {25/9}-3/2 + {5/2}-1 = 1

Q.

Evaluate: 30³ + 20³ – 50³.

1. 36000

2. -90000

3. 15000

4. 90000

Q.

Question 50

Fill in the blanks to make the statement true.

$3\times (-1)\times (-15)=$___ .

Q.

Question 129

Fill in the blank to make the statement true.

125 + (68+17) = (125+.........) +17

Q. Find the product.
(i) $\sqrt{3}\times \sqrt{7}$

(ii) $\sqrt[3]{11}\times \sqrt{10}$

(iii) $\sqrt[4]{12}\times \sqrt[7]{16}$

(iv) $\sqrt[3]{2}\times \sqrt[4]{3}$

(v) $\sqrt[3]{3}\times \sqrt[6]{2}$

Q.

Find the value of ( 109 )²

1. 18181

2. 18811

3. 11881

4. 11181

Q. Prove that ${\left(\frac{81}{16}\right)}^{-3/4}\times \left\{{\left(\frac{25}{9}\right)}^{-3/2}÷{\left(\frac{5}{2}\right)}^{-3}\right\}=1$.

Q. show that there is no integer a such that a^2-3a-19 is divisible by 289.

Q. Find the product.
(i) $\sqrt[3]{2}\times \sqrt[3]{3}\times \sqrt[3]{4}$

(ii) $\sqrt[3]{3}\times \sqrt{3}\times \sqrt[3]{2}$

(iii) $\sqrt[3]{2}\times \sqrt[4]{2}\times \sqrt{2}$

(iv) $2\times \sqrt[3]{4}\times 3\times \sqrt[3]{16}$

(v) $3\times \sqrt[3]{32}\times 3\times \sqrt{4}$

Q. If $\frac{\left(4+\sqrt{5}\right)}{\left(4-\sqrt{5}\right)}=\left(a+b\sqrt{5}\right)$, find the values of a and b.

Q. Evaluate:
(i) (49)^1/2
(ii) (125)^1/3
(iii) (64)^1/6

Q. Evaluate using suitable identities :
(90097)³

Q. 104 × 96 = ?
(a) 9864
(b) 9984
(c) 9684
(d) 9884

Q. Evaluate:
(i) (99)²
(ii) (998)²

Q. Evaluate:
(i) (25)^3/2
(ii) (32)^2/5
(iii) (81)^3/4

Q.

Name the property represented.

$4\times 0=0$

Q.

(28)²+(–15)²+(–13)²