What is #4sqrt42 + 2sqrt28  sqrt7#?
Write each of the radicands as a product of the factors:
Split the roots into separate roots.
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To simplify the expression ( 4\sqrt{42} + 2\sqrt{28}  \sqrt{7} ):

First, simplify the square roots where possible:
 ( \sqrt{42} = \sqrt{2 \times 21} = \sqrt{2} \times \sqrt{21} )
 ( \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} = 2\sqrt{7} )

Substitute the simplified square roots back into the expression: ( 4\sqrt{42} + 2\sqrt{28}  \sqrt{7} = 4\sqrt{2} \times \sqrt{21} + 2(2\sqrt{7})  \sqrt{7} )

Combine like terms: ( 4\sqrt{2} \times \sqrt{21} + 2(2\sqrt{7})  \sqrt{7} = 4\sqrt{2} \times \sqrt{21} + 4\sqrt{7}  \sqrt{7} )

Simplify further: ( 4\sqrt{2} \times \sqrt{21} + 4\sqrt{7}  \sqrt{7} = 4\sqrt{42} + 3\sqrt{7} )
So, ( 4\sqrt{42} + 2\sqrt{28}  \sqrt{7} ) simplifies to ( 4\sqrt{42} + 3\sqrt{7} ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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