Prime Factorisation

Q. Question 68

Count the number of cubes in the given shapes.

Q. 2744 written as a product of its primes is

1. $2\times 2\times 2\times 7\times 7$ ​
2. $2\times 2\times 7\times 7\times 7$
3. $2\times 2\times 7\times 7$
4. $2\times 2\times 2\times 7\times 7\times 7$

Q.

A cube is painted red along all its faces and then divided into 27 smaller identical pieces. How many of the resultant pieces will have no face painted?

1. 3

2. 2

3. 1

4. 9

Q. Fill the missing number in the factor tree diagram.

Q.

Number of unit cubes in the following solid is:

1. 8

2. 14

3. 11

4. 10

Q. Factorise the following numbers into primes.
(i) 32
(ii) 57
(iii) 23
(iv) 150
(v) 216
(vi) 208
(vii) 765
(viii) 342
(ix) 377
(x) 559

Q.

Express each of the following as product of powers of their prime factors:

$\left(i\right)$ $648$ $\left(ii\right)$ $405$

$\left(iii\right)$ $540$ $\left(iv\right)$ $3,600$

Q.

With what number should 1715 be divided to get a perfect cube?

1. 2

2. 7

3. 5

4. Already a perfect cube

Q. Question 84

Find the number of cubes in the base layer of the following figure.

Q. Prove that if a number is tripled then its cube is 27th time the cube of the given number.

Q. Use the sign of >, < or = in the box to make the statements true.
$(-8)+(-4)\square (-8)-(-4)$

Q. Which one of the following cannot be the difference between the squares of any two conecutive natural numbers or in other words, two consecutive perfect squares?

1. 731
2. 2003
3. 1029
4. 1146

Q.

Question 9

In which of the following expressions, prime factorization has been done:
24 = $2\times 3\times 4$
56 = $7\times 2\times 2\times 2$
70 = $2\times 5\times 7$
54 = $2\times 3\times 9$

Q. The total surface area of a cube is 294 sq m. What is the volume of this cube?

Q. Which of the following expressions is equivalent to ${(-x)}^{\frac{1}{5}}$?

1. $-\frac{1}{5x}$
2. $-\frac{1}{x^5}$
3. $\frac{1}{\sqrt[5]{5-x}}$
4. $-\sqrt[5]{5x}$

Q. If $\frac{5+\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$, then -

1. $a=-11,b=6$
2. $a=6,b=11$
3. $a=11,b=-6$
4. $a=23,b=-13$

Q. Expand:
${(\left(\frac{3}{4}\right)x+\left(\frac{2}{9}\right)y)}^2$

Q. Simplified form of
${[\sqrt[3]{3x^{4}y}\times \frac{1}{\sqrt[4]{4x^2{y}^8}}]}^{-6}$

1. $\frac{y^{10}}{x^5}$
2. $\frac{y^2}{x}$
3. $x^5.y^{10}$
4. $\frac{y^5}{x^5}$

Q. 11 × 11 × 11 × 11 × 11 = ${11}^5$

1. True
2. False