Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

(i) 64

(ii) 144

(iii) 4489

(iv) 27225

(v) 390625

Answer :

We know that if n is number of digits in a perfect square number, then it's square root will have \(\frac{n}2\) digits if n is even and \{\frac{(n+1)}2\) digits if n is odd.

(i) 64

Here n is even i.e, 2.

So, number of digits in \(\sqrt{64} = \frac { 2 }{ 2 } = 1\)

(ii) 144

Here n is odd i.e, 3.

So, number of digits in square root = \(\frac { 3+1 }{ 2 } = 2\)

(iii) 4489

Here n is even i.e, 4.

Number of digits in square root =\( \frac { 4 }{ 2 } = 2\)

(iv) 27225

Here n is odd i.e, 5.

Number of digits in square root =\( \frac { 5+1 }{ 2 } = 3\)

(iv) 390625

Here n is even i.e, 6.

So, number of digits in square root =\( \frac { 6 }{ 2 } = 3\)

- 1.Find the square root of each of the following numbers by Long Division method. (i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 (ix) 576 (x) 1024 (xi) 3136 (xii) 900
- 3.Find the square root of the following decimal numbers. (i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36
- 4.Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. (i) 402 (ii) 1989 (iii) 3250 (iv) 825 (v) 4000
- 5.Find the least number which must be added to each of the following numbers so as to get a perfect square. Also, find the square root of the perfect square so obtained. (i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412
- 6.Find the length of the side of a square whose area is \(441 m^2\)
- 7.In a right triangle ABC, ∠B =\( 90^{\circ}\). (a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB
- 8.A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain the same. Find the minimum number of plants he needs more for this.
- 9.There are 500 children in a school. For a P.T. drill, they have to stand in such a manner that the number of rows is equal to the number of columns. How many children would be left out in this arrangement?

- NCERT solutions for class 8 maths chapter 1 Factorisation and Mensuration
- NCERT solutions for class 8 maths chapter 1 Rational Numbers
- NCERT solutions for class 8 maths chapter 1 Factorization
- NCERT solutions for class 8 maths chapter 2 Linear Equations in One Variable
- NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals
- NCERT solutions for class 8 maths chapter 4 Practical Geometry
- NCERT solutions for class 8 maths chapter 5 Data Handling
- NCERT solutions for class 8 maths chapter 6 Squares and Square Roots
- NCERT solutions for class 8 maths chapter 7 Cube and Cube Roots
- NCERT solutions for class 8 maths chapter 8 Comparing Quantities
- NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities
- NCERT solutions for class 8 maths chapter 10 Visualising Solid Shapes
- NCERT solutions for class 8 maths chapter 11 Mensuration
- NCERT solutions for class 8 maths chapter 12 Exponents and Powers
- NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions
- NCERT solutions for class 8 maths chapter 14 Factorization
- NCERT solutions for class 8 maths chapter 15 Introduction to Graphs
- NCERT solutions for class 8 maths chapter 16 Playing with Numbers

- NCERT solutions for class 8 science chapter 1 Crop Production & Management
- NCERT solutions for class 8 science chapter 2 Microorganisms: Friend and Foe
- NCERT solutions for class 8 science chapter 3 Synthetic Fibers and Plastics
- NCERT solutions for class 8 science chapter 4 Materials: Metals and Nonmetals
- NCERT solutions for class 8 science chapter 5 Coal and Petroleum
- NCERT solutions for class 8 science chapter 6 Combustion and Flame
- NCERT solutions for class 8 science chapter 7 Conservation of Plants and Animals
- NCERT solutions for class 8 science chapter 8 Cell-Structure and Function
- NCERT solutions for class 8 science chapter 9 Reproduction in Animals
- NCERT solutions for class 8 science chapter 10 Reaching the Age of Adolsence
- NCERT solutions for class 8 science chapter 11 Force and Pressure
- NCERT solutions for class 8 science chapter 12 Friction
- NCERT solutions for class 8 science chapter 13 sound
- NCERT solutions for class 8 science chapter 14 Chemical Effects of Electric Current
- NCERT solutions for class 8 science chapter 15 Some Natural Phenomena
- NCERT solutions for class 8 science chapter 16 Light
- NCERT solutions for class 8 science chapter 17 Stars and the Solar System
- NCERT solutions for class 8 science chapter 18 Pollution of Air and Water