
Find the number of digits in the square root of each of the following numbers (without calculator).
(i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625
Answer
509.7k+ views
12 likes
Hint: To determine the number of digits in the square root of a number, first we have to determine that the total number of digits in the given number is odd or even. If the total number of digits in the number is even then, the number of digits in square root will be determined by using the formula and in the case of odd number of digits square root will be where, is the number of digits in the number.
Complete step-by-step answer:
(i) Number of digits in 64 is 2 so,
Since is even so,
Numbers of digits in square root in the square root of 64 is:
Hence, the total number of digits in the square root of 64 is 1.
(ii) Number of digits in 144 is 3 so,
Since is odd so,
Number of digits in square root of 144 is:
Hence, the total number of digits in the square root of 144 is 2.
(iii) Number of digits in 4489 is 4 so,
Since is even so,
Numbers of digits in square root of 4489 is:
Hence, the total number of digits in the square root of 4489 is 2.
(iv) Number of digits in 27225 is 5 so,
Since is odd so,
Number of digits in square root of 27225 is:
Hence, the total number of digits in the square root of 27225 is 3.
(v) Number of digits in 390625 is 6 so,
Since is even so,
Number of digits in square root of 390625 is:
Hence, the total number of digits in the square root of 390625 is 3.
Note: Count the numbers of digits in the given number and determine whether even or odd. The method is applicable only for a perfect square number.
Complete step-by-step answer:
(i) Number of digits in 64 is 2 so,
Since
Numbers of digits in square root in the square root of 64 is:
Hence, the total number of digits in the square root of 64 is 1.
(ii) Number of digits in 144 is 3 so,
Since
Number of digits in square root of 144 is:
Hence, the total number of digits in the square root of 144 is 2.
(iii) Number of digits in 4489 is 4 so,
Since
Numbers of digits in square root of 4489 is:
Hence, the total number of digits in the square root of 4489 is 2.
(iv) Number of digits in 27225 is 5 so,
Since
Number of digits in square root of 27225 is:
Hence, the total number of digits in the square root of 27225 is 3.
(v) Number of digits in 390625 is 6 so,
Since
Number of digits in square root of 390625 is:
Hence, the total number of digits in the square root of 390625 is 3.
Note: Count the numbers of digits in the given number and determine whether even or odd. The method is applicable only for a perfect square number.
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Science: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Class 9 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Given that HCF 306 657 9 find the LCM 306 657 class 9 maths CBSE

The highest mountain peak in India is A Kanchenjunga class 9 social science CBSE

What is pollution? How many types of pollution? Define it

Differentiate between the Western and the Eastern class 9 social science CBSE
