# Surd and Indices

**Vedic Maths trick to calculate Surd and Indices.**

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Q.1) If ^{a}/_{b} = ^{c}/_{d} = ^{2}/_{5} , then evaluate : -
**[a**^{4} + c^{4} / b^{4} + d^{4}]^{1/4}

Let ^{a}/_{b} = ^{c}/_{d} = ^{2}/_{5} = k ....................(1)

^{a}/_{b} = ^{c}/_{d} = k

a = bk , c = dk

According to the question put the power of 4

a^{4} = k^{4}b^{4}....................(2)

c^{4} = k^{4}d^{4}....................(3)

Add equation (2) and (3)

a^{4} + c^{4} = k^{4}b^{4} + k^{4}d^{4}

a^{4} + c^{4} = k^{4}(b^{4} + d^{4})

a^{4} + c^{4} / b^{4} + d^{4} = k^{4}....................(4)

putting the value from equation (4)

[a^{4} + c^{4} / b^{4} + d^{4}]^{1/4} = [k^{4}]^{1/4}

Now from equation (1)

^{2}/_{5} = k

** k = **^{2}/_{5}

^{a}/

_{b}=

^{c}/

_{d}=

^{2}/

_{5}

^{4}+ c

^{4}/ b

^{4}+ d

^{4}]

^{1/4}

^{2}/

_{5}