Question

Find the value of √10+√15/√2​

Answer 1

Rewrite −15-15 as −1(15)-115.√−1(15)⋅√10-115⋅10Rewrite √−1(15)-115 as √−1⋅√15-1⋅15.√−1⋅√15⋅√10-1⋅15⋅10Rewrite √−1-1 as ii.i⋅√15⋅√10i⋅15⋅10Multiply ii by √1515 to get i√15i15.i√15⋅√10i15⋅10Multiply i√15i15 by √1010 to get i√15√10i1510.i√15√10i1510Simplify i√15√10i1510.

i√150i150Rewrite 150150 as 52⋅652⋅6.

i√52⋅6i52⋅6Pull terms out from under the radical.i(5√6)i56Simplify the expression.

5i√6

Answer 2

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Rewrite −15-15 as −1(15)-115.√−1(15)⋅√10-115⋅10Rewrite √−1(15)-115 as √−1⋅√15-1⋅15.√−1⋅√15⋅√10-1⋅15⋅10Rewrite √−1-1 as ii.i⋅√15⋅√10i⋅15⋅10Multiply ii by √1515 to get i√15i15.i√15⋅√10i15⋅10Multiply i√15i15 by √1010 to get i√15√10i1510.i√15√10i1510Simplify i√15√10i1510.

i√150i150Rewrite 150150 as 52⋅652⋅6.

i√52⋅6i52⋅6Pull terms out from under the radical.i(5√6)i56Simplify the expression.

5i√6