Question

Write one sentence describing the square roots of numbers such as √0.6, which is less than 1.

Write another sentence describing the square roots of numbers such as StartRoot 1.6 EndRoot, which is greater than 1.

Answer 1

The specialty of square root of numbers less than 1 is that the square root will be greater than the number itself.

The specialty of square root of numbers greater than 1 is that the square root will be less than the number itself.

        ( i ) Number less than 1

• Any number less than 1 can be written in the form :
• A whole number/ $10^{n}$
• So when we square the number, it will be :
• ( whole Number)²/$10^{2n}$ =  Number²/$100^{n}$
• As number of digits in the whole number increases n also increase.
• Always : Whole number  < $10^{n}$
• Since power of 10 also increases the number will become smaller and smaller.
• Hence square root will become larger.

       ( i i ) Number greater than 1

• For numbers greater than 1 , if we represent in fractional form,
• Numerator > Denominator
• Then squaring makes number bigger and bigger.
• Hence square root will become smaller.