Sample Problems

Question 1: What are the two square roots of 100?

Solution:

Here 100 is the perfect square of 10, so this can have two roots one negative and one positive

or we can say real square root of 100 is ±10

or              10² = 10 × 10 = 100

             (-10)² = – 10 × – 10 = 100

Hence, the two square roots of 100 are +10 and -10.

Question 2: What are the square roots of 12?

Solution: 

Square root of 12 

Here 12 is not a perfect square so this number doesn’t have two square roots we can’t write it as √12 = ±3.464

Therefore √12 = 3.464 is an irrational number, the numbers that are not a perfect square are members of the irrational numbers. This means that numbers or square roots can’t be written as the quotient of two integers.

Question 3: What are the two square roots of 144? 

Solution: 

square root of 144

Here square root of 144 is perfect square of 12, i.e a whole number this has two square roots +12, -12

Therefore √144 = ± 12

The arithmetic value which is used for representing the quantity and used in making calculations are defined as Numbers. A symbol like “4,5,6” which represents a number is known as a numeral. Without numbers, we can’t do counting of things, dates, time, money, etc., these numbers are also used for measurement and used for labelling.

The properties of numbers make them helpful in performing arithmetic operations on them. These numbers can be written in numeric forms and also in words.

For example, 3 is written as three in words, 35 is written as thirty-five in words, etc. Students can write the numbers from 1 to 100 in words to learn more.

There are different types of numbers, which we can learn. They are whole and natural numbers, odd and even numbers, rational and irrational numbers, etc.