Wurzeln: √3 + 1/5√18 - 1/4√48 + 1/7√72

Question

√3 + 1/5√18 - 1/4√48 + 1/7√72

3√5 * 4√5

Answer 1

√ 3 + ( 1 / 5 ) √ 18 - ( 1 / 4 ) √ 48 + ( 1 / 7 ) √ 72
= √ 3 + ( 1 / 5 ) √ ( 2 * 9 ) - ( 1 / 4 ) √ ( 3 * 16 ) + ( 1 / 7 ) √ ( 8 * 9 )
= √ 3 + ( 1 / 5 ) * 3 * √ 2 - ( 1 / 4 ) * 4 * √ 3 + ( 1 / 7 ) * 3 * √ 8
= √ 3 + ( 1 / 5 ) * 3 * √ 2 - √ 3 + ( 1 / 7 ) * 3 * √ 8
= ( 1 / 5 ) * 3 * √ 2 + ( 1 / 7 ) * 3 * √ 8
= ( 1 / 5 ) * 3 * ( 1 / 2 ) * √ ( 2 * 4 ) + ( 1 / 7 ) * 3 * √ 8
= ( 3 / 10 ) * √ 8 + ( 3 / 7 ) * √ 8
= ( ( 21 / 70 ) + ( 30 / 70 ) ) * √ 8
= ( 51 / 70 ) * √ 8
= ( 51 / 70 ) * √ ( 2 * 4 )
= ( 51 / 70 ) * 2 * √ 2
= ( 51 / 35 ) * √ 2

3 √ 5 * 4 √ 5
= 12 * 5
= 60