Find the least number by which 147 must be multiplied so that it becomes perfect square

4

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

147 = 72 × 3

To make the unpaired 3 into paired, multiply the number with 3

Therefore,

147 × 3 = 72 × 32

Hence, square root of number =

= 21

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square.

Question:

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

Solution:

The prime factorisation of 147:

147 = 3 x 7 x 7

Grouping the factors into pairs of equal factors, we get:

147 = 3 x (7 x 7)

The factor, 3 does not have a pair. Therefore, we must multiply 147 by 3 to make a perfect square. The new number is:

(3 x 3) x (7 x 7) = 441

Taking one factor from each pair on the LHS, the square root of the new number is 3 x 7, which is equal to 21.

Jump to

• Squares and Square Roots Exercise 3.1
• Squares and Square Roots Exercise 3.2
• Squares and Square Roots Exercise 3.3
• Squares and Square Roots Exercise 3.4
• Squares and Square Roots Exercise 3.5
• Squares and Square Roots Exercise 3.6
• Squares and Square Roots Exercise 3.7
• Squares and Square Roots Exercise 3.8
• Squares and Square Roots Exercise 3.9

• Rational Numbers
• Powers
• Squares and Square Roots
• Cube and Cube Roots
• Playing with Numbers
• Algebraic Expressions and Identities
• Factorization
• Division of Algebraic Expressions
• Linear Equation in One Variable
• Direct and Inverse Variations
• Time and Work
• Percentage
• Profit Loss Discount and Value Added Tax
• Compound Interest
• Understanding Shapes Polygons
• Understanding Shapes Quadrilaterals
• Understanding Shapes Special Types Quadrilaterals
• Practical Goemetry
• Visualising Shapes
• Area of Trapezium and Polygon
• Volume Surface Area Cuboid Cube
• Surface Area and Volume of Right Circular Cylinder
• Classification And Tabulation Of Data
• Classification And Tabulation Of Data Graphical Representation Of Data As Histograms
• Pictorial Representation Of Data As Pie Charts Or Circle Graphs
• Data Handling Probability
• Introduction To Graphs

RD Sharma Solutions Class 8 Mathematics Solutions for Squares and Square Roots Exercise 3.4 in Chapter 3 - Squares and Square Roots

Question 4 Squares and Square Roots Exercise 3.4

Find the smallest number by which 147 must be multiplied so that it becomes a perfect square. Also, find the square root of the number so obtained.

Answer:

Firstly let’s find the prime factors for

147 = (7 × 7) × 3

=72 × 3

To make the unpaired 3 into paired, multiply the number with 3

147 × 3 = 72 × 32

∴ Square root of √ (147 × 3) = 7 × 3

= 21

Video transcript

hello students welcome to leader learning question and answer videos now to understand the relation between these two terms let's first discuss what do we mean by thrust and what do we mean by pressure and automatically we will derive the relation so what is thrust thrust is nothing but a force which is applied normal to the surface so normal or perpendicular to the surface so the force let me write that down is the force applied in direction in a direction which is which is normal or perpendicular normal means perpendicular to the surface so as you can see in this picture which we have here if you apply the force directly like this so the effect will be much larger and the nail will get embedded much faster so that will be the thrust this is an example of thrust now let's talk about pressure now we know that pressure is given as the formula force upon area the unit is newton per meter square newton for force and meter square is for area which is also called one pascal now we know this is pressure how do we make find out what is the relation between thrust and pressure so pressure is if i say pressure is per unit thrust on a surface so if i say pressure is equal to the thrust or the force when the area is one meter square then am i saying anything wrong here so pressure is nothing but per unit thrust on the surface so it is equal to the thrust or the force when area is one meter square so greater is the force so if f is greater then pressure will also be greater or greater the thrust more will be the pressure similarly if thrust is less so lesser the thrust pressure will also be lesser so it's proportionally directly proportional to the thrust right so more is the thrust more will be the pressure lesser is the thrust less will be the pressure i hope this was clear from what i made you understand the picture here as well so if you have any further doubts please post your comments below thank you

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