Clearly, this number 64 doesn't consist of any irrational term like square root or cube root or any higher degree root. So, number 64 is not a surd.
64 is a perfect square number which can be obtained by the square of 8. Hence, the square root of 64 is a rational number. In this mini-lesson, we will learn to find the square root of 64 along with solved examples.
What is the Square Root of 64? The square root of 64 is 8, i.e. √64 = 8. The radical representation of the square root of 64 is √64. Also, we know that the square of 8 is 64, i.e. 82 = 8 × 8 = 64.
When we can't simplify a number to remove a square root (or cube root etc) then it is a surd. Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd! not? The surds have a decimal which goes on forever without repeating, and are Irrational Numbers.
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In Mathematics, surds are the values in square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified.
So for example, √7 is a surd, and as it is irrational, its decimal expansion would go on forever without a recurring pattern. Note that square roots of decimals or fractions are not always surds. For example, √6.25=2.5 which is rational and therefore not a surd.
The number underneath this radical symbol is known as radicand. Hence, the number whose square root is to be determined is called the radicand. In this case, 8 is the radicand and 2√2 is the simplest and the radical form of √8. This value is called surd since you cannot simplify this further.
The number -64 has no real square roots.
Because 64 is a negative number is does not have any real square roots as both ' and produce 64 as an answer.
Since 64 is a perfect cube, therefore it is easy to find its cube root, but for imperfect cubes we have to estimate the values. But it sometimes becomes difficult to evaluate.
⟹ 64 is both perfect square and perfect cube number.
Factors of 64: 1, 2, 4, 8, 16, 32, 64.
In mathematics
64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number. 64 is also the first whole number (greater than 1) that is both a perfect square and a perfect cube.
But √6 , 3√2 , √20 do not have proper roots. These number forms are termed as surds.
In Mathematics, the square root of 15 is a number that when multiplied by itself yields the original number 15. Because it cannot be stated in the form of p/q, the square root of 15 is an irrational number.
The square root of 12 is represented in the radical form as √12, which is equal to 2√3. Since 2√3 cannot be further simplified, hence such roots are called surds.
For example, √9 is a surd because it cannot be simplified to 3/3 or any other rational number.
The square root of 50, 7.0710678…, is an irrational number since it is a non-terminating decimal.
The square root of 20 is represented as √20, where √ is the radical sign and 20 is said to be radicand. In the simplest form, the √20 can be written as 2√5. Therefore, here we cannot say that √20 is a rational number since √5 is an irrational number.
Which is an irrational number. Facts: Square root of 18 is a not a natural or a whole number but an irrational number.
The square root of 23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.