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If you are expected to calculate it without a calculator then the first step is to write the fraction as a ratio - a top heavy one if necessary. You will find that the numerator and denominator of the rational fraction are both perfect square numbers. Then the square root of the ratio is the ratio of the square roots.
For example, to find the square root of 11.11... recurring.
You know that, since it is a recurring decimal, the number is rational.
In ratio form, this number is 100/9 and so
sqrt(11.11...) = sqrt(100/9) = sqrt(100)/sqrt(9) = 10/3 = 3.33... recurring.
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Is the square root of 729 rational?
The square root of 729 is 27.Yes, it is a rational number because 27 can be written as simple fraction, 27/1.
Is the square root of 36 rational or irrational?
The square root of 36 is 6 which is a rational number because it can be expressed as an improper fraction in the form of 6/1
Is the square root of 38 a rational number?
No because it can't be expressed as a fraction
Is the square root of 0.144 rational?
Well, honey, the square root of 0.144 is approximately 0.12, which is a rational number because it can be expressed as a fraction (12/100). So, yes, the square root of 0.144 is indeed rational. Hope that clears things up for ya!
Is the square root of 47 a rational number?
'47' is a prime number, so it does not have a rational square root. sqrt(47) = 6.8556546... to 9 d.p. An irrational number which cannot be converted to a quotient; that is made into a fraction. NB The square roots of prime numbers are irrational.
