Square Root Of 64 Rational Or Irrational

First let us see what happens when we square a rational number.

Square root of 64 rational or irrational.

Is the square root of 66 rational or irrational. To determine if a number is rational you need to see if you can write the value exactly as a fraction or ratio of two integers. It is an irrational number if it is not a perfect square. The positive square root of 64 is 8 and all integers are rational by definition.

Let me explain. Rational 2 is 1 2 repeating decimal rational or irrational. 33 is not a perfect 5th power. Enter number you would like to test for you can enter sqrt 50 for square roots or 5 4 for exponents or 6 7 for fractions.

This means that the answer to the square root of 66 will have an infinite number of decimals. But the 5th root of 33 is irrational. So this looks like at least for this example is going to be irrational and let s see if a was square root of two negative 24 plus the square root of two well once again i m not doing a proof here but intuitively this is going to be a decimal it s going to have a decimal expansion that s going to go on forever and never repeat and so. It is a perfect square with answer exactly 8the square root of 64 is the integer 8 8 x 8 64 so it is rational.

Since 66 is not a perfect square it is an irrational number. Thus the 5th root of 32 is rational because 32 is a 5th power namely the 5th power of 2. Rational every repeating decimal is rational. Nth roots of a k are irrational unless k is a multiply of n.

But some numbers cannot be written as a ratio. D square root of 3 5 e 2 3 in the same way we saw that only the square roots of square numbers are rational we could prove that only the nth roots of nth powers are rational. It is a perfect square with answer exactly 8the square root of 64 is the integer 8 8 x 8 64 so it is rational. Every non repeating decimal is irrational all whole numbers are rational.

All fractions are rational. The square root of 66 is a rational number if 66 is a perfect square. Is 64 squared rational or irrational. Squaring a rational number.

If the rational number is a b then that becomes a 2 b 2 when squared. The number 8 can be written exactly.