simplify each of the following
a. 5√16*5√2
b. 4√243/4√3
c. (3+√2)(4+√7)
d. (√3-√2)²
Answers
Step-by-step explanation:
(i) Given
As x is positive real number then we have
Hence the simplified value of is
(ii) Given
As x and y are positive real numbers then we can write
By using law of rational exponents we have
Hence the simplified value of is
(iii) Given
As x and y are positive real numbers then we have
By using law of rational exponents we have
By using law of rational exponents we have
(x−23y−12)2=1x23+23×1y12+12=1x43×1y22=1x43×1y=1x43y
Hence the simplified value of is .
(iv) (x−−√)−23 y4−−√ ÷ xy−12−−−−−√=(x12)−23 (y4)12 ÷ (x × y−12)12=x12×−23 × y4×12x12 × y−12×12 =x−13 × y2x12 × y−14by using the law of rational exponents, am ÷ an = am−n, we have x−13−12 × y2+14=x−56 × y94 =y94x56(v). 243 x10 y5 z10−−−−−−−−−−−√5=(243 × x10 × y5 × z10)15=(243)15 × (x10)15 × (y5)15 × (z10)15=(35)15 × x10×15 × y5×15 × z10×15=3 × x2 × y × z2=3x2yz2(vi) (x−4y−10)54=(x−4)54(y−10)54=x−4×54y−10×54=x−5y−252=y252x5
(vii) (2√3√)5(67)2
(2√3√)5(67)2=(2√3√)2+2+1(67)2=(2√3√)2×(2√3√)2×(2√3√)1×(67)2=(23)×(23)×(2√3√)1×(67)2
=(23)×(23)×(2√3√)1×(67)2=162√493√=5127203−−−−√=(5127203)12
Answer:
this is the solved answer
