help me solve this please
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Answer:
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- Final result is equal to 5√2 .
To Find :- from image we have to find End result .
Solution :-
→ Start = √5
Step 1) :-
→ √5 × 3 = 3√5 ----- Equation (1)
Step 2) :-
→ Equation (1) + 2√5
→ 3√5 + 2√5
→ 5√5 ------- Equation (2)
Step 3) :-
→ Equation (2) × 4√3
→ 5√5 × 4√3
→ (5 × 4) × (√5 × √3)
using √a × √b = √(ab)
→ 20√15 ------- Equation (3)
Step 4) :-
→ Equation (3) ÷ 10√5
→ 20√15 ÷ 10√5
→ (20 ÷ 10) × (√15 ÷ √5)
using √a ÷ √b = √(a ÷ b)
→ 2√3 ------- Equation (4)
Step 5) :-
→ Equation (4) - 6√3
→ 2√3 - 6√3
taking √3 common,
→ √3(2 - 6)
→ √3 × (-4)
→ (-4√3) ------- Equation (5)
Step 6) :-
→ Equation (5) × √7
→ (-4√3) × √7
→ (-4) × (√3 × √7)
using √a × √b = √(ab)
→ (-4) × √21
→ (-4√21) ------- Equation (6)
Step 7) :-
→ Equation (6) + 10√21
→ (-4√21) + 10√21
taking √21 common,
→ √21(-4 + 10)
→ √21 × 6
→ 6√21 ------- Equation (7)
Step 8) :-
→ Equation (7) ÷ 3√3
→ 6√21 ÷ 3√3
→ (6 ÷ 3) × (√21 ÷ √3)
using √a ÷ √b = √(a ÷ b)
→ 2√7 ------- Equation (8)
Step 9) :-
→ Equation (8) - 5√7
→ 2√7 - 5√7
taking √7 common,
→ √7(2 - 5)
→ √7 × (-3)
→ (-3√7) ------- Equation (9)
Step 10) :-
→ Equation (9) × √8
→ (-3√7) × √8
→ (-3) × (√7 × √8)
using √a × √b = √(ab)
→ (-3) × √56
→ (-3√56) ------- Equation (10)
Step 11) :-
→ Equation (10) + 21√14
→ (-3√56) + 21√14
→ {(-3) × √(14 × 4)} + 21√14
→ {(-3) × √(14 × 2 × 2)} + 21√14
→ {(-3) × √(14 × 2²)} + 21√14
using √(a²) = a ,
→ {(-3) × 2√14)} + 21√14
→ [{(-3) × 2} × √14] + 21√14
→ (-6√14) + 21√14
taking √14 common,
→ √14(-6 + 21)
→ √14 × 15
→ 15√14 ------- Equation (11)
Step 12) :-
→ Equation (11) ÷ 3√7
→ 15√14 ÷ 3√7
→ (15 ÷ 3) × (√14 ÷ √7)
using √a ÷ √b = √(a ÷ b),
→ 5 × √2
→ 5√2 = End .
Hence, 5√2 comes in the end box .
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