Maddiie
In a paragraph, describe how to simplify each expression.
16 1/2
Square root 100
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Harkirat
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?????????
why don't u use the equation box to write yr question...
Maddiie
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In a paragraph, describe how to simplify each expression.
16 1/2
\[\sqrt{100}\]
Harkirat
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is the first one
\[16^{1/2}\] ???
Maddiie
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yes
Harkirat
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pls note that \[x ^{1/2} = \sqrt{x}\]
Maddiie
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why is that
Harkirat
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okay I will explain thru an example...
Maddiie
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ok awesome
Harkirat
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u know that
\[\sqrt{4}= 2\]
also
\[(4)^{1/2} = (2^{2})^{1/2} = 2^{2*1/2} = 2^{1}=2\]
Harkirat
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so we find that \[\sqrt{4} = (4)^{1/2}\]
because both give same result i.e. 2
Maddiie
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\[({8}^2)\]
Maddiie
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confused
Harkirat
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so we can solve the first one as
\[(16)^{1/2} = (4^{2})^{1/2} = 4^{2*1/2} = 4^{1}=4\]
Harkirat
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what is confusing u???
Maddiie
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Oh because 4x4=16 right
Harkirat
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yes
Maddiie
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So \[\sqrt{100}= 10 \]
heromiles
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You might want to introduce and include rules of exponents and roots as part of your explanation.
Harkirat
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yes that is correct
Maddiie
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ok i understood the steps now
Maddiie
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ok i understood the steps now
Harkirat
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see square and root are opposite operations. so when they occur together, they cancel each other out....
we can show the working for root100 as follows :
\[\sqrt{100}=\sqrt{10^{2}}=10\]
the square inside and root outside cancel each other out
Harkirat
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are u familiar with exponential laws???
Maddiie
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makes sense
Maddiie
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not really but i can try to find it in my book
Harkirat
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yes, u shud have all the laws in front of you and slowly try to learn them by heart....
Maddiie
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ok thank u
Harkirat
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u r welcome, just keep in mind...
\[\sqrt{x}=x ^{1/2}\]
\[\sqrt[3]{x}=x ^{1/3}\]
\[\sqrt[4]{x}=x ^{1/4}\]
and so on....