Question

√18-√32+√72= √72+√50-√162= √200-√8-√50= √128+√18-√98=

Answer 1

√18-√32+√72=√9*2-√16*2+√36*2=3√2-4√2+6√2=√2(3-4+6)=5√2
√72+√50-√162=√36*2+√25*2-√81*2=6√2+5√2-9√2=√2(6+5-9)=2√2
√200-√8-√50=√100*2-√4*2-√25*2=10√2-2√2-5√2=√2(10-2-5)=3√2
√128+√18-√98=√64*2+√9*2-√49*2=8√2+3√2-7√2=√2(8+3-7)=4√2

Answer 2

We can simplify each expression by finding perfect squares that are factors of each term and then combining like terms:

√18 - √32 + √72 = √9 * 2 - √16 * 2 + √36 * 2 = 3√2 - 4√2 + 6√2 = 5√2

√72 + √50 - √162 = √36 * 2 + √25 * 2 - √81 * 2 * 2 = 6√2 + 5√2 - 9√2 = 2√2

√200 - √8 - √50 = √100 * 2 - √4 * 2 - √25 * 2 = 10√2 - 2√2 - 5√2 = 3√2

√128 + √18 - √98 = √64 * 2 + √9 * 2 - √49 * 2 = 8√2 + 3√2 - 7√2 = 4√2

Therefore,

√18 - √32 + √72 = 5√2 √72 + √50 - √162 = 2√2 √200 - √8 - √50 = 3√2 √128 + √18 - √98 = 4√2.