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Question Number 24840 by kosarrr last updated on 27/Nov/17

Commented by prakash jain last updated on 27/Nov/17

Please use an app called camscanner to post pictures of written/printed material. Your picture is very hard to read.

$$\mathrm{Please}\:\mathrm{use}\:\mathrm{an}\:\mathrm{app}\:\mathrm{called}\:\mathrm{camscanner} \\ $$$$\mathrm{to}\:\mathrm{post}\:\mathrm{pictures}\:\mathrm{of}\:\mathrm{written}/\mathrm{printed} \\ $$$$\mathrm{material}. \\ $$$$\mathrm{Your}\:\mathrm{picture}\:\mathrm{is}\:\mathrm{very}\:\mathrm{hard}\:\mathrm{to}\:\mathrm{read}. \\ $$

Answered by behi.8.3.4.17@gmail.com last updated on 27/Nov/17

a)5(√5)×3(√(125))=5(√5)×3(√(25×5))=5×3×(√(25))×(√5)×(√5)= =5×3×5×(√5^2 )=5×3×5×5=375 b)(√(75))/(√3)=((√(75))/(√3))=((√(25×3))/(√3))=((√(5^2 ×3))/(√3))=((5(√3))/(√3))=5 c)3(√(63))+2(√(28))=3(√(9×7))+2(√(4×7))= =3(√(3^2 ×7))+2(√(2^2 ×7))=3×3(√7)+2×2(√7)= =9(√7)+4(√7)=13(√7) d)3(√8)+5(√(18))−2(√(50))=3(√(4×2))+5(√(9×2))−2(√(25×2))= =3(√(2^2 ×2))+5(√(3^2 ×2))−2(√(5^2 ×2))= =3×2(√2)+5×3(√2)−2×5(√2)= =6(√2)+15(√2)−10(√2)=11(√2) ■

$$\left.\boldsymbol{{a}}\right)\mathrm{5}\sqrt{\mathrm{5}}×\mathrm{3}\sqrt{\mathrm{125}}=\mathrm{5}\sqrt{\mathrm{5}}×\mathrm{3}\sqrt{\mathrm{25}×\mathrm{5}}=\mathrm{5}×\mathrm{3}×\sqrt{\mathrm{25}}×\sqrt{\mathrm{5}}×\sqrt{\mathrm{5}}= \\ $$$$=\mathrm{5}×\mathrm{3}×\mathrm{5}×\sqrt{\mathrm{5}^{\mathrm{2}} }=\mathrm{5}×\mathrm{3}×\mathrm{5}×\mathrm{5}=\mathrm{375} \\ $$$$\left.\boldsymbol{{b}}\right)\sqrt{\mathrm{75}}/\sqrt{\mathrm{3}}=\frac{\sqrt{\mathrm{75}}}{\sqrt{\mathrm{3}}}=\frac{\sqrt{\mathrm{25}×\mathrm{3}}}{\sqrt{\mathrm{3}}}=\frac{\sqrt{\mathrm{5}^{\mathrm{2}} ×\mathrm{3}}}{\sqrt{\mathrm{3}}}=\frac{\mathrm{5}\sqrt{\mathrm{3}}}{\sqrt{\mathrm{3}}}=\mathrm{5} \\ $$$$\left.\boldsymbol{{c}}\right)\mathrm{3}\sqrt{\mathrm{63}}+\mathrm{2}\sqrt{\mathrm{28}}=\mathrm{3}\sqrt{\mathrm{9}×\mathrm{7}}+\mathrm{2}\sqrt{\mathrm{4}×\mathrm{7}}= \\ $$$$=\mathrm{3}\sqrt{\mathrm{3}^{\mathrm{2}} ×\mathrm{7}}+\mathrm{2}\sqrt{\mathrm{2}^{\mathrm{2}} ×\mathrm{7}}=\mathrm{3}×\mathrm{3}\sqrt{\mathrm{7}}+\mathrm{2}×\mathrm{2}\sqrt{\mathrm{7}}= \\ $$$$=\mathrm{9}\sqrt{\mathrm{7}}+\mathrm{4}\sqrt{\mathrm{7}}=\mathrm{13}\sqrt{\mathrm{7}} \\ $$$$\left.\boldsymbol{{d}}\right)\mathrm{3}\sqrt{\mathrm{8}}+\mathrm{5}\sqrt{\mathrm{18}}−\mathrm{2}\sqrt{\mathrm{50}}=\mathrm{3}\sqrt{\mathrm{4}×\mathrm{2}}+\mathrm{5}\sqrt{\mathrm{9}×\mathrm{2}}−\mathrm{2}\sqrt{\mathrm{25}×\mathrm{2}}= \\ $$$$=\mathrm{3}\sqrt{\mathrm{2}^{\mathrm{2}} ×\mathrm{2}}+\mathrm{5}\sqrt{\mathrm{3}^{\mathrm{2}} ×\mathrm{2}}−\mathrm{2}\sqrt{\mathrm{5}^{\mathrm{2}} ×\mathrm{2}}= \\ $$$$=\mathrm{3}×\mathrm{2}\sqrt{\mathrm{2}}+\mathrm{5}×\mathrm{3}\sqrt{\mathrm{2}}−\mathrm{2}×\mathrm{5}\sqrt{\mathrm{2}}= \\ $$$$=\mathrm{6}\sqrt{\mathrm{2}}+\mathrm{15}\sqrt{\mathrm{2}}−\mathrm{10}\sqrt{\mathrm{2}}=\mathrm{11}\sqrt{\mathrm{2}}\:\:\:\:\blacksquare \\ $$

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