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Surd, Roots and Radicals, How they compare - Coggle Diagram
Surd, Roots and Radicals
Surds
A surd is an expression that includes a square root, cube root or other root symbol. Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form. The surds have a decimal which goes on forever without repeating, and are Irrational Numbers.
Example
The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified. If we further simply them, we get decimal values, such as: √2 = 1.4142135…
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Roots
The root of a number in math is a number that when multiplied by itself produces the original number.
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Radicals
In maths, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.
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How they compare
If "a" is a rational number and "n" is a positive integer such that the "nth" root of "a" is an irrational number, then a1/n is called a surd or radical and a root is a symbol that can give a solution to an equation. It is usually expressed as a number or algebraic formula.
They are all similar in that they all work with square roots.