Question 165033
Hi, Hope I can help,
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simplify the following radical expressions the square root of x times the square root of x
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Here is the problem you are trying to solve
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{{{ sqrt (x) * sqrt (x) }}}

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We first have to know what square roots are
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To find the square root of something, we are trying to find a number you can square (multiply twice) to get the number, {{{ x^2 = 16 }}}, you are trying to find "x", this case it would be {{{ 4 }}}, ( or {{{ -4 }}}, if you are using negative square roots) 
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Examples: find {{{ sqrt (25) }}}, the answer would be {{{ 5 }}}, since you can multiply 5 twice ( or square "5" ) to get 25, {{{ 5(5) = 25 }}}, or {{{ 5^2 = 25 }}}
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find {{{ sqrt (81) }}}, the answer would be {{{9 }}}, you can multiply "9" twice to get "81", you can also square "9" to get "81", {{{ 9(9) = 81 }}}, or {{{ 9^2=81 }}}
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If you multiply a square root of a number by itself( or square it), it will always equal the number in the square root sign.
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Examples: {{{ sqrt (49)*sqrt(49) }}} = {{{ (7)(7) }}} = {{{ 49 }}}
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  {{{ sqrt (64)*sqrt(64) }}} = {{{ 8(8) }}} = {{{ 64 }}} ( number in the sqrt sign )  
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 {{{ sqrt (1/4) * sqrt (1/4) }}} = {{{ (1/2)(1/2) }}} = {{{ 1/4 }}} (same number that is in square root sign)
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{{{ sqrt (33)*sqrt(33) }}} (We don't know the exact square root, but from the examples, we know the answer would be {{{ 33 }}}, because {{{ (sqrt (33))^2 = 33 }}} )( The answer is the number inside the square root sign, or "33")
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Lets do the original question.
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 simplify the following radical expressions the square root of x times the square root of x
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{{{ sqrt (x) * sqrt (x) }}}, this is the same as all the examples, except that it is a letter.( It doesn't change the way we solve this problem though )
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If the answer is the number( or letter) inside the square root sign
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The answer would be {{{ x }}}, since it is inside the square root sign. 
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To find the square root of a number, you would need to find a number multiplied by itself, or squared to get that number (or letter). So since we found the square root of "x" ( {{{ sqrt (x) }}} ), and we are multiplying by the same number, we are saying {{{ (sqrt (x))^2 }}}, which would be equal to "x"
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The simplified number/variable/expression would be {{{x}}}
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Your answer is {{{ x }}}
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Hope I helped,Levi