Simplify:((frac{10sqrt{3}}{sqrt{5}} – sqrt{15}))2

Simplify:((frac{10sqrt{3}}{sqrt{5}} – sqrt{15}))²

Correct Answer: Option B

Explanation

Note that (frac{10sqrt{3}}{sqrt{5}} = frac{10sqrt{3}}{sqrt{5}} times – frac{sqrt{5}}{sqrt{5}})
= (frac{10sqrt{15}}{sqrt{5}} = 2sqrt{15})
hence, ((frac{10sqrt{3}}{sqrt{5}} – sqrt{15}))² = ((2sqrt{15} – sqrt{15}))²
= ((2sqrt{15} – sqrt{15}))((2sqrt{15} – sqrt{15}))
= 4(sqrt{15 times 15} – 2sqrt{15 times 15} – 2sqrt{15 x 15} + sqrt{15 times 15})
= 4 x 15 – 2 x 15 – 2 x 15 + 15
= 60 – 30 – 30 + 15
= 15