first, consider that 25 = 5^2, and -25 = -1*25 = -1*5^2.
Then, you can write:
![\sqrt[]{-25}=\sqrt[]{(-1)(25)}=\sqrt[]{(-1)(5^2)}=5\sqrt[]{-1}=5i](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B-25%7D%3D%5Csqrt%5B%5D%7B%28-1%29%2825%29%7D%3D%5Csqrt%5B%5D%7B%28-1%29%285%5E2%29%7D%3D5%5Csqrt%5B%5D%7B-1%7D%3D5i)
because i = √-1.
Hence, the answer is 5i
Answer:
Step-by-step explanation:
ABCD is a parallelogram. AB is produced to P, such that AB = BP and PQ is drawn parallel to BC to meet AC produced at Q. Given AB = 8 cm, AD = 5 cm, AC = 10 cm.
→ BC ║ QP →→Given
In Δ ABC and ΔAPQ
∠ABC=∠APQ→→[BC ║ QP , BP is a transversal, so corresponding angles are equal]
∠BAC=∠PAQ→→Reflex angle
Δ ABC ~ ΔAPQ→→(AA similarity criterion]
When triangles are similar, their corresponding angles are equal.
AC=CQ=10 cm, shows that point C is mid point of AQ.
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Let the required number be x, then 10 + x/6 = 5
x/6 = 5 - 10 = -5
x = 6 x -5 = -30
x = -30
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