simplify (root3+root7)the whole square write the order of the following surds 4root10 and 5 root 9 express 5 - Maths - Number Systems

Question

simplify (root3+root7)the whole square
write the order of the following surds
4root10 and 5 root 9
express 5 root1280 in simplest form
simplify 5 root 288/625
simplify 4root 28 divided by 3 root 7
please say me soon with steps

Aakash Sharma · Accepted Answer

$(1) (\sqrt{3} + \sqrt{7})^{2} = (\sqrt{3})^{2} + (\sqrt{7})^{2} + 2 \times \sqrt{3} \times \sqrt{7} = 3 + 7 + 2 \sqrt{3 \times 7} = 10 + 2 \sqrt{21} = 2 (5 + \sqrt{21})$

$(2) order of 4 \sqrt{10} is 2 and order of 5 \sqrt{9} = 5 \times 3 = 15 is 1$

$(3) 5 \sqrt{1280} = 5 \times \sqrt{2^{8} \times 5} = 5 \times 2^{4} \sqrt{5} = 5 \times 16 \sqrt{5} = 80 \sqrt{5}$

$(4) 5 \sqrt{\frac{288}{625}} = 5 \sqrt{\frac{2^{5} 3^{2}}{5^{4}}} = \frac{5 \times 2^{2} \times 3 \sqrt{2}}{5^{2}} = \frac{12 \sqrt{2}}{5}$

$(5) \frac{4 \sqrt{28}}{3 \sqrt{7}} = \frac{4 \sqrt{2^{2} \times 7}}{3 \sqrt{7}} = \frac{4 \times 2 \sqrt{7}}{3 \sqrt{7}} = \frac{8}{3}$

simplify (root3+root7)the whole square. write the order of the following surds 4root10 and 5 root 9. express 5 root1280 in simplest form simplify 5 root 288/625. simplify 4root 28 divided by 3 root 7 please say me soon with steps

simplify (root3+root7)the whole square.

write the order of the following surds

4root10 and 5 root 9.

express 5 root1280 in simplest form

simplify 5 root 288/625.

simplify 4root 28 divided by 3 root 7

please say me soon with steps