Question

1. Using prime factorisation, find the square roots of (a)11025 (b) 4761
2. Using prime factorisation, find the cube roots of (a)512 (b) 2197
3. Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.
4. Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.
5. Write two Pythagorean triplets each having one of the numbers as 5.
6. By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.
7. By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.
8. Find the square root of the following by long division method. (a)1369 (b) 5625 104. Find the square root of the following by long division method. (a)27.04 (b) 1.44
9. What is the least number that should be subtracted from 1385 to get a perfect square? Also find the square root of the perfect square. 106. What is the least number that should be added to 6200 to make it a perfect square?
10. Find the least number of four digits that is a perfect square. 108. Find the greatest number of three digits that is a perfect square
11. Find the least square number which is exactly divisible by 3, 4, 5, 6 and 8. 110. Find the length of the side of a square if the length of its diagonal is 10cm.
12. A decimal number is multiplied by itself. If the product is 51.84, find the number. 112. Find the decimal fraction which when multiplied by itself gives 84.64
13.Find three numbers in the ratio 2:3:5, the sum of whose squares is 608.
15. Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
16. The diagonals of a rhombus are 8 cm and 15 cm. Find its side.
17. Two adjacent angles of a parallelogram are in the ratio 1:3. Find its angles.
18. Of the four quadrilaterals— square, rectangle, rhombus and trapezium— one is somewhat different from the others because of its design. Find it and give justification.
In each of the questions, 1 to 4write the correct answer from the given four options.
1. 196 is the square of (a) 11 (b) 12 (c) 14 (d) 16
2. Which of the following is a square of an even number? (a) 144 (b) 169 (c) 441 (d) 625
3. A number ending in 9 will have the units place of its square as
(a) 3 (b) 9 c) 1 (d) 6
4.Which of the following will have 4 at the units place?
(a) 142 (b) 622 (c) 272 (d) 352

Answer 1

Answer:

Step-by-step explanation:

1. Using prime factorisation, find the square roots of (a)11025 (b) 4761

11025 = 3 *  3 *  5 * 5 * 7 * 7

11025 = 3² * 5² * 7²

11025 = ( 3* 5 * 7)²

√11025 = 3 * 5 * 7 = 105

4761  = 3 * 3 * 23 * 23

√4761 = 3*23 = 69

2. Using prime factorisation, find the cube roots of (a)512 (b) 2197

512 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

512 = 2³ * 2³ * 2³

512 = 8³

∛512 = 8

2197 = 13 * 13 * 13

∛2197 = 13

3. Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

176 = 2 * 2 * 2 * 2 * 11

176 = 2² * 2² * 11

176 is not a perfect square

176 to be multiplied by 11 to get a perfect square

176 * 11 = 2² * 2² * 11²

4. Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

9720 = 2 * 2 * 2 * 3 * 3 * 3 * 3 * 3 * 5

9720 = 2³ * 3³ * 3 * 3 * 5

9720 is not a perfect cube

9720 should be multiplied with 3 * 5 * 5 = 75 to get Perfect cube

9720 * 75 = 2³ * 3³ * 3³ * 5³

Answer 2

Answer:

13.

Let the three numbers be 2k, 3k, 5k

Given:

$(2k)^2+(3k)^2+(5k)^2=608$

$4k^2+9k^2+25k^2=608$

$38k^2=608$

$k^2=\frac{608}{38}$

$k^2=16$

$k=4$

$\therefore$The required numbers are 8, 12, 20

17.

Concept:

Adjacent angles of a parallelogram are supplementary.

Let ABCD be the given parallelogram

Given:

∠A=k and ∠B=3k

Then,

∠A + ∠B=180°

k+3k=180°

4k=180°

k=45°

⇒

∠A =45,° ∠B=135°, ∠C =45,° ∠D=135°