Question #2bca3

2 Answers
Tamir E.
Nov 19, 2017

See below

Explanation:

Laws:
1) #x^(1/2)=sqrt(x) iff sqrt(x)=x^(1/2)#
2) #x^a*x^b=x^(a+b) iff x^(a+b)=x^a*x^b#
2) #x^a/x^b=x^(a-b)#

#2/sqrt(2)=?#

First:
#2=2^1#
#=> 2^1=2^((1/2+1/2))#
#=> 2^(1/2+1/2)=2^(1/2)*2^(1/2)#

Second:
#2^(1/2) iff sqrt(2)#

and therefore:
#2/sqrt(2)=(2^(1/2)*2^(1/2))/(2^(1/2))=2^(1/2)=sqrt(2)#

Fleur
Nov 19, 2017

See below.

Explanation:

#2/sqrt2# has a radical in its denominator. If we want to remove the radical, we can multiply the expression by #sqrt2/sqrt2#. This is essentially the same as multiplying by #1#, so we aren't changing the value of the expression.

#2/sqrt2 *sqrt2/sqrt2#

#sqrt2 * sqrt2# is simply #2#. Thus, we have

#(2sqrt2) / 2#

We can now cancel the #2# in the numerator and denominator.

#(cancel2sqrt2) / cancel2 = sqrt2#

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