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# Surds and Indices Questions and Answers

**Surds and Indices Questions**

Go through the entire page to know how to solve Surds and Indices Questions and Answers using easy formulas.

**Surds**

**Surds are the figures left in ‘square root or cube form.’ They are consequently irrational numbers. The number left in the form of square root or cube root form because in decimal form such value goes on forever. Furthermore, the square roots of figures, which do not have precise square roots, are known as Surds.**

__Laws of Surds__**b√p = p(1/b)**

**b√pq = b√p * b√q**

**√(p/q) = (b√p )/(b√q )**

**(b√p)^b = p**

**a √b√p = ab√p**

**(b√p)^a = b√p^a**

**Indices**

**Indices denote the power at which a particular figure is raised. The index of a number shows the number of times a figure is used in multiplication, or it shows that a figure is recurrently multiplied by itself. It is shown as small number to the right-hand side and directly above the base number.**

__Laws of Indices__**(p^a)^b = p^ab**

**(pq)^b = p^bq^b**

**p^a/p^b = p^a-b**

**(p/q)^b = p^b/q^b**

**p^-1 = 1/p**

**Formula or Rule for solving Surds and Indices Questions and Answers**

- A number that is raised to the power zero will always be equals to one. For instance a0 = 1.
- Surd b√p can be solved further only if the factor of p is a perfect square.
- If surds are included in the denominator of a fraction, then it is required to rationalize the denominator through multiplying both denominator and numerator by an associated surd.
- In solving the equations related to surd, it is essential to understand that every surd is an irrational number
- Every irrational number is not a surd.
- It is necessary to rationalize the denominator and to eliminate the surd in order to simplify different expressions.
- In indices, the multiplication rule for solving the question with same base, the formula used is x^a * x^b = x^a+b
- For division with same base formula used: x^a / x^b = (x)^a-b
- Multiplication rule for same indices: x^a * y^a = (x*y)^a
- Division rule for same indices: x^a / y^a = (x/y)^a
- The square root or cube root of a positive real number is known as a surd only if its value is not exactly determined.
- Two simple quadratic surd’s sum and difference are known as complementary surds to one another.
- If m and n are both rational numbers and √p and √q are both surds and m + √p = n + √q then m = n and p = q
- If m – √p = n – √q then m = n and p = q.
- If m + √p = 0, then m = 0 and p = 0.
- If m – √p = 0, then m = 0 and p = 0.