Menthal map Surd,Roots and Radicals

Definition

A surd is an Expression that includes a square root,cube root or other root symbol.

Surd

Use

Surds are used to write irrational numbers precisely.In real life Surds are used to make sure that important calculations are precise,for example by engineers building Bridges.

Properties

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Rule 1: = √(rs) = √r√s.

Rule 2: √(r/s) = √r/√s.

Rule 3: r/√s = (r/√s) X (√s/√s)

Rule 4: p√r ± q√r.

Rule 5: r / (p+q√n)

Rule 6: r / (p-q√n)

Example

For example the square root of 3 and the cube root of 2 are both surds. 5 ≈ 2.23606 \sqrt{5} \approx 2.23606 5 ≈2.23606, which is an irrational number. The square root of 5 is a surd.

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Formula

The root of a number in math is a number that when multiplied by itself produces the original number.

Roots

Definition

the square root of 49 is 7 because 7×7=49. In this case, because 7 is multiplied by itself twice to produce 49, we call 7 the square root of 49.

Example

A perfect square root exists for a perfect square number only. The square root of an even perfect square is even. An odd perfect square will have an odd square root. A perfect square cannot be negative and hence the square root of a negative number is not defined.

Properties

Definition

Radical

A radical expression is an expression containing a square root. Radicand is a number or expression inside the radical symbol. Radical equation is An equation containing radical expressions with variables in the radicands.

Example

√2,3√72,√2x+7, and 4√1p. 2 , 72 3 , 2 x + 7

All exponents in the radicand must be less than the index. Any exponents in the radicand can have no factors in common with the index. No fractions appear under a radical. No radicals appear in the denominator of a fraction.

Properties

Julyses López