2025 क सभ प रम ख क रक क य ह ? Sqrt 2025 क म न क य ह ?

उत तर:

क प रम ख क रक # 2025 = 5xx5xx3xx3xx3xx3 #

#sqrt (2025) = 45 #

स पष ट करण:

यह 2045 क ल ए एक अपघटन प ड ह

#color (सफ द) ("xxxxxx") र ग (न ल) (2025) #

#color (सफ द) ("xxxxxxx") darr #

#color (सफ द) ("xxxx") "-------------" #

#color (सफ द) ("XXX") darrcolor (सफ द) ("xxxxxx") darr #

#color (सफ द) ("XXX") र ग (ल ल) 5color (सफ द) ("XX") xxcolor (सफ द) ("XX") 405 #

#color (सफ द) ("xxxxxxxxxxx") darr #

#color (सफ द) ("XXXXXXXXX") "-----------" #

#color (सफ द) ("XXXXXXXX") darrcolor (सफ द) ("xxxx") darr #

#color (सफ द) ("XXXXXXXXX") र ग (ल ल) 5color (सफ द) ("x") xxcolor (सफ द) ("x") 81 #

#color (सफ द) ("XXxxxxxxxxxxxX") darr #

#color (सफ द) ("xxxxxxxxxxx") "--------------" #

#color (सफ द) ("XXXXXXXXXX") darrcolor (सफ द) ("xxxxxx") darr #

#color (सफ द) ("xxxxxxxxxxx") 9color (सफ द) ("XX") xxcolor (सफ द) ("XX") 9 #

#color (सफ द) ("XXXXXXXXXX") darrcolor (सफ द) ("xxxxxx") darr #

#color (सफ द) ("XXXXXXXXX") "------" र ग (सफ द) ("xxx.x") "------" #

#color (सफ द) ("XXXXXXXX") darrcolor (सफ द) ("x") darrcolor (सफ द) ("xxx") darrcolor (सफ द) ("x") darr #

# र ग (सफ द) ("XXxxxxXX") र ग (ल ल) 3 xx र ग (ल ल) 3 र ग (सफ द) ("xxxx" र ग (ल ल) 3 xxcolor (ल ल) 3 #)

त हम र प स # 2025 = र ग (ल ल) 5 ^ 2xxcolor (ल ल) 3 ^ 2xxcolor (ल ल) 3 ^ 2 #

#color (सफ द) ("XXX") = (र ग (ल ल) 5xxcolor (ल ल) 3xxcolor (ल ल) 3) 2 ^ #

#color (सफ द) ("XXX") = 45 ^ 2 #

इसल य

#color (सफ द) ("XXX") sqrt (2025) = sqrt ((45 ^ 2)) = 45 #

क य ह (sqrt (5+) sqrt (3)) / (sqrt (3+) sqrt (3+) sqrt (5)) - (sqrt (5-) sqrt (3)) / (sqrt (3+) sqrt (3) sqrt (5))?

2/7 हम ल त ह , A = (sqrt5 + sqrt3) / (sqrt3 + sqrt3 + sqrt5) - (sqrt5-sqrt3) / (sqrt3 + sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5 + sqrt3) -sqrt3) / ((2sqrt3-sqrt5) = (sqrt5 + sqrt3) / (2sqrt3 + sqrt5) - (sqrt5-sqrt3) / (2sqrt3-sqrt5) = ((sqrt5 + sqrt3) - (sqrt5 + sqrt3) (2sqrt3-sqrt5) - (sqrt5 + sqrt5) ) (2sqrt3 + sqrt5)) / ((2sqrt3 + sqrt5) (2sqrt3-sqrt5) = ((2sqrt15-5 + 2 * 3-sqrt15) - (2sqrt15 + 5-2 * 3-sqrt15)) ((2sqrt3) ^ 2- (sqrt5) ^ 2) = (रद द कर (2sqrt15) -5 + 2 * 3cancel (-sqrt15) - रद द कर (2sqrt15) -5 + 2 * 3 + रद द (sqrt15) = (12-5) = ( -10 + 12) / 7 = 2/7 ध य न द क , यद भ जक म ह (sqrt3 +

आप क स सरल करत ह (1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) div sqrt (a + 1) / ( (a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)), a> 1?

व श ल गण त प र र पण ...> र ग (न ल ) (((1 / sqrt (a-1) + sqrt (a + 1)) / (1 / sqrt (a + 1) -1 / sqrt (a-1)) ) / (sqrt (a + 1) / ((a-1) sqrt (a + 1) - (a + 1) sqrt (a-1)) = color (ल ल) ((1 / sqrt (a) 1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a-1))) / (sqrt ( +1) / (sqrt (a-1) cdot sqrt (a-1) cdot sqrt (a + 1) -sqrt (a + 1) cdot sqrt (a + 1) sqrt (a-1)) (र ग) न ल ) (((1 / sqrt (a-1) + sqrt (a + 1)) / ((sqrt (a-1) -sqrt (a + 1)) / (sqrt (a + 1) cdot sqrt (a) -1))) / (sqrt (a + 1) / (sqrt (a + 1) cdot sqrt (a-1) (sqrt (a-1) -sqrt (a + 1)) = color (ल ल) ((1 / sqrt (a-1) + sqrt (a + 1)) / ((sq

अभ व यक त क सरल बन ए ?: 1 / (sqrt (144) + sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169))

1 पहल न ट क : 1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / ((sqrt (n + 1) + sqrt (n)) () sqrt (n + 1) -sqrt (n)) र ग (सफ द) (1 / (sqrt (n + 1) + sqrt (n)) = (sqrt (n + 1) -sqrt (n)) / () n + 1) -n) र ग (सफ द) (1 / (sqrt (n + 1) + sqrt (n)) = sqrt (n + 1) -sqrt (n) So: 1 / (sqrt (144) +) sqrt (145)) + 1 / (sqrt (145) + sqrt (146)) + ... + 1 / (sqrt (168) + sqrt (169)) = (sqrt (145) -sqrt (144)) + (sqrt (146) -sqrt (145)) + ... + (sqrt (169) -sqrt (168)) = sqrt (169) -sqrt (144) = 13-12 = 1