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What is the square root of 6 (7 the square root of 3 + 6)?

Answer 1

Ethan Adkins

#21sqrt2 + 6sqrt6, or 3(7sqrt2 + 2sqrt6)#

the square root of #6# can be written as #sqrt6#.

#7# multiplied by the square root of #3# can be written as #7sqrt3#.

#6# added to #7# multiplied by the square root of #3# can be written as #7sqrt3 + 6#

therefore the square root of #6 *# (#7# multiplied by the square root of #3#)# + 6#) is written as #sqrt6(7sqrt3+6)#.

to solve #sqrt6(7sqrt3+6)#, multiply the two terms in the bracket separately with the term outside the bracket.

#sqrt6 * 7sqrt3 = 7 * (sqrt6 * sqrt3) = 7 sqrt18#

#sqrt18 = sqrt9 * sqrt2 = 3 * sqrt2#

#7 * sqrt18 = 7 * 3 * sqrt2 = 21 * sqrt2#

#sqrt6 * 7sqrt3 = 21sqrt2#

#sqrt6 * 6 = 6sqrt6#

#sqrt6(7sqrt3+6) = (sqrt6 * 7sqrt3) + (sqrt6 * 6)#

#= 21sqrt2 + 6sqrt6#

the roots cannot be simplified further, but you may wish to factorise:

#21sqrt2 = 3 * 7sqrt2#

#6sqrt6 = 3 * 2sqrt6#

#21sqrt2 + 6sqrt6 = 3(7sqrt2 + 2sqrt6)#

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Answer 2

Ethan Adkins

The square root of 6 multiplied by the quantity 7 times the square root of 3 plus 6 is equal to 42 times the square root of 3 plus 36.

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Answer from HIX Tutor

When evaluating a one-sided 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.