What's Square root of 5184?
3 Answers
Explanation:
Given;
Demonstrating an intelligent guess approach.
Explanation:
Lets take an 'informed' shot in the dark.
The last digit is 4 and we know that
so we could have 2 as our last digit of the root. Using ? to represent the the next digit to the left we have
Consider the
Putting our guess together we have
Check - splitting the 72 into 70+2
Explanation:
Given
First find the prime factorisation:
#5184 = 2 * 2592#
#color(white)(5184) = 2^2 * 1296#
#color(white)(5184) = 2^3 * 648#
#color(white)(5184) = 2^4 * 324#
#color(white)(5184) = 2^5 * 162#
#color(white)(5184) = 2^6 * 81#
#color(white)(5184) = 2^6 * 3 * 27#
#color(white)(5184) = 2^6 * 3^2 * 9#
#color(white)(5184) = 2^6 * 3^3 * 3#
#color(white)(5184) = 2^6 * 3^4#
Note that all of the factors occur an even number of times, so the square root is exact...
#sqrt(5184) = sqrt(2^6 * 3^4) = 2^3 * 3^2 = 72#