Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 1 Numbers Ex 1.5 Textbook Questions and Answers, Notes.

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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers Ex 1.5

Question 1.

Fill in the blanks

(i) The ones digits in the cube of 73 is __________ .

Answer:

7

(ii) The maximum number of digits in the cube of a two digit number is __________ .

Answer:

6

(iii) The smallest number to be added to 3333 to make it a perfect cube is __________ .

Answer:

42

(iv) The cube root of 540×50 is __________ .

Answer:

30

(v) The cube root of 0.000004913 is __________ .

Answer:

0.017

Question 2.

Say True or False.

(i) The cube of 24 ends with the digit 4.

Answer:

True

(ii) Subtracting 103 from 1729 gives 93.

Answer:

True

(iii) The cube of 0.0012 is 0.000001728.

Answer:

False

(iv) 79570 is not a perfect cube.

Answer:

True

(v) The cube root of 250047 is 63.

Answer:

True

Question 3.

Show that 1944 is not a perfect cube.

Answer:

1944 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3

= 2^{3} × 3^{3} × 3 × 3

There are two triplets to make further triplets we need one more 3.

∴ 1944 is not a perfect cube.

Question 4.

Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube.

Answer:

We have 10985 = 5 × 13 ×13 × 13

= 5 × 13 ×13 × 13

Here we have a triplet of 13 and we are left over with 5.

If we divide 10985 by 5, the new number will be a perfect cube.

∴ The required number is 5.

Question 5.

Find the smallest number by which 200 should be multiplied to make it a perfect cube.

Answer:

Grouping the prime factors of 200 as triplets, we are left with 5 × 5

We need one more 5 to make it a perfect cube.

So to make 200 a perfect cube multiply both sides by 5.

1000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5

Now 1000 is a perfect cube.

∴ The required number is 5.

Question 6.

Find the cube root 24 × 36 × 80 × 25.

Answer:

Question 7.

Find the cube root of 729 and 6859 prime factorisation.

Answer:

(i)

= 3 × 3

\(\sqrt[3]{729}\) = 9

(ii) \(\sqrt[3]{6859}\) = \(\sqrt[3]{19 \times 19 \times 19}\)

\(\sqrt[3]{6859}\) = 19

Question 8.

What is the square root of cube root of 46656?

Answer:

We have to find out \(\sqrt{(\sqrt[3]{46656})}\)

First we will find \(\sqrt[3]{46656}\)

∴ The required number is 6.

Question 9.

If the cube of a squared number is 729, find the square root of that number.

Answer:

(729)^{1/3} = 3 × 3 = 9

∴ The cube of 9 is 729.

9 = 3 × 3 [ie 3 is squared to get 9]

We have to find out √3,

√3 = 1.732

Question 10.

Find two smallest perfect square numbers which when multiplied together gives a perfect cube number.

Answer:

Consider the numbers 2^{2} and 4^{2}

The numbers are 4 and 16.

Their procluct 4 × 16 = 64

64 = 4 × 4 × 4

∴ The required square numbers are 4 and 16